Friday, April 13, 2007

Math Nerd #1

Personally, I find that puzzles such as these constitute my favorite type of idle time activity. The elegant ones which reveal the simplicity of a mathematical solution to a stated problem, or ones which involve thinking "out of the box" provide one with an "AHA!" experience, and often prompt the response, "Now why didn't I think of that before?"

1. Divide the figure shown at left into (a) three equal, congruent pieces that are exactly alike. Once you accomplish this very simple and obvious task, try to divide the same figure into (b) four identical, congruent pieces that are exactly alike.

2. You have nine coins and a pan balance. One coin is counterfeit, and although it looks identical to all the others, it weighs slightly more
than the others. Find the counterfeit coin in three weighings. As a corollary, answer whether it is possible to accomplish the task in only two weighings.

3. Copy this diagram and insert the numerals 1 through 8 in the circles, so no two consecutive integers are in circles directly connected by purple lines.


4. Arrange the numerals 1 1 2 2 3 3 4 4 so a number will be formed in which the ones are separated by one digit, the twos by two digits, the threes by three digits, and naturally, the fours by four digits.

5. The total number of squares in figures A to C is given. Find the total number of squares in figures D & E. An additional problem (for those of mathematical bent only,) is to discover the mathematical relationship between the base number of squares, and the number of squares in total in each figure.

6. Use the numbers in the set N = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 } to complete each set A, B and C so that each lettered set totals 27, and all 10 numerals in N are used only once. Once done, repeat the procedure to get a total of 22 per letter set.






















Answers
1. a)
b)

3. One possible solution is:2. Put a random coin aside from the 9, place 4 of the remaining coins on one side of the balance, the other four on the other pan. If it balances, the counterfeit coin is the one you selected & put aside... problem solved. If one pan shows heavier, you know the fake coin is in that pile of four. Take two coins out of this pile and place one each on the two pans on the ut how to figure out which of 3 coins is slightly heavier with the last weighing, can't you?balance; if they are equal in weight, remove those coins - they are good. Take the last two coins and repeat for the third weighing; one of them will weigh more: it is counterfeit.
Yeah, it can be accomplished in just two weighings: take out three coins and set aside, place three of the remaining six coins on one balance pan, the other three on the other pan. Weigh. If one side is heavier, that pan contains three coins, one of which must be counterfeit; if both pans are equal, the fake coin must be in the lot set aside. Surely you can figure o


4. One arrangement is: 4 1 3 1 2 4 3 2.
5. Well, fig. A, B, & C have 1, 5 and 14 separate squares (as stated). D has a total of 30 and E has 55. Mathematically stated, A has 1 base square, so take 1 squared = 1, which is the number of contained squares. B has 2 base squares, so take 2 squared, or 4, and add the previous number, which was 1, for a total of 5. C had three base squares, so square three, which is nine, then add the previous number (5), for a total of 14 total squares. D has 4 base squares, so squared we have 16, and adding the previous number of 14, we get 30 total squares. Last, E has 5 base squares, so square 5 to get 25, and add 30 from the previous to get 55 total squares!
You can see that if F was drawn, it would amount to 91 total squares, right?
6. For each set A, B and C to have numbers adding to 27, choose one of:
a) b)
And for the sets A, B and C to add to 22, try this one:

Tongue Twister Time

Amazing how difficult it is to sling together groups of similar sounding words (not necessarily homonyms) in a sentence and say it repeatedly. Although different than Spoonerisms, the results are often hilarious. Try saying any of the following three times, quickly:

1. How much wood would a woodchuck chuck if a woodchuck could chuck wood?

2. Red rubber baby buggy bumpers.

3. The sinking steamer sunk.

4. She sells seashells by the seashore in the Seychelles.

5. Toy boat or Troy boat. (Repeat 6 times, quickly)

6. The sixth sick sheik's sixth sheep's sick.

7. If a three month truce is a truce in truth, is the truth of a truce in truth a three month truce?

8. If you stick a stock of liquor in your locker,
It is slick to stick a lock upon your stock,
Or some joker who is slicker's going to trick you of your liquor
If you fail to lock your liquor with a lock.

9. The skunk sat on the stump;
The skunk thunk the stump stunk
But the stump thought the skunk stunk.

10. Six gray geese in a green field grazing.

11. Six slick, slim saplings.

12. Six thick thistle sticks.

13. A cup of coffee in a copper coffeepot.

14. Round and round the rugged rock the ragged rascal ran.

15. Theophilus Thistledown, the successful thistle sifter, in sifting a sieve full of unsifted thistles, thrust three thousand thistles through the thick of his thumb.
If then Theophilus Thistledown, the successful thistle sifter, in sifting a sieve full of unsifted thistles thrust three thousand thistles through the thick of his thumb, see that thou, in sifting a sieve full of unsifted thistles, dost not get the thistles stuck in thy tongue.




Thursday, April 12, 2007

Word Nerd #2

Thought-provoking questions to stimulate students to dive into a dictionary or thesaurus; not a bad exercise.

1. There is at least one English word in which a single vowel is repeated 6 times. What is it?

2. What animal name of 9 letters is pronounced in one syllable?

3. What English word of 7 letters contains 8 separate words in it(without rearranging any letters.)

4. What English word of 8 letters has only a single vowel in it?

5. What 5 letter English word contains four personal pronouns, with the letters in the same order?

6. Make seven even without subtracting an odd number from it.
















Answers
1. Indivisibility
2. daschund
3. Therein
4. Strength
5. Usher (us, she, he, her)
6. Remove the letter s

Wednesday, April 11, 2007

Mind Bender #3

I like to call this the World's Easiest Quiz, but take care... most people get less than half of these right.

1. Adam and Eve were banished from the Garden of Eden for eating what fruit?

2. In what year of our present calendar was Christ born?

3. Was Charles Lindbergh the first person to cross the Atlantic Ocean by air? Or was he the third, fifth, fourteenth, or what?

4. Boris Karloff gained his greatest fame playing a weird character in the movies. Who was the character he is best known for?

5. What was the highest title that Julius Caesar acquired: king, emperor, dictator or consul?

6. Which of the following rid Ireland of snakes?
a) The Royal Zoological Society
b) Nobody - there never were any snakes in Ireland
c) Irish terriers
d) St. Patrick

7. How much more reflected light do we get from a full moon than from a half moon?
a) The same amount
b) Twice as much
c) Four times as much
d) Seven times as much

8. How long did the Hundred Years War last?

9. In which country are Panama hats made?

10. Where do we get catgut?

11. What exactly are moleskin trousers made of?

12. What kind of creatures were the Canary Islands named after?

13. What was King George VI's first name?

14. What is a camel's hair brush made of?

15. How long did the Thirty Years War last?

16. Louis XVIII was the last one, but how many previous kings of France were called Louis?

17. What color is a purple finch?

18. For what crime was Captain Kidd, the infamous pirate, hanged?

19. How were most of the "witches" put to death in Salem, Massachusetts?

20. Is the earth closer, or farther away from the sun in winter?

21. Are there, or should there be any punctuation marks in the greeting, and Christmas Carol 'GOD REST YE MERRY GENTLEMEN'?

22. Christmas is also referred to as Xmas. Is the latter an irreverent or reverent way of describing this seasonal holiday?



Answers
1. The bible only refers to the fruit of "the tree of the knowledge of good and evil." If you suggested an apple, you are just as incorrect as if you had thought papaya.
2. Scholars believe He was born between 8BC and 4BC. The monk Dionysius, in the 6th Century erroneously calculated the birth date of Christ; this was subsequently disproved.
3. Lindy made the first non-stop SOLO flight across the Atlantic, but in fact he was merely the 119th person to cross the pond by air.
4. Frankenstein's monster. Dr. Frankenstein was the mad scientist who assembled his monster out of used parts.
5. Julius Caesar was made dictator for life, but never emperor. The Roman Empire was formed years after Brutus' famous soliloquy.
6. Noone did; there never were any snakes in Ireland.
7. About 7 times as much. At full moon, the sun's rays shine straight down on the part we get to see as a full moon so none of the surface is in shadow; at half-moon, the sun strikes the moon's surface obliquely and the moon's tall mountains shadow much of the surface.
8. One hundred sixteen years (1337-1453). Look it up! Historians aren't good at math.
9. Panama hats are mostly made in Ecuador, and small 'trim' items are sometimes added in Panama. Ecuador is the country of origin, though.
10. 'Catgut', formerly in wide use in tennis racquets, comes from the intestines of sheep or horses, never from cats.
11. Moleskin is a cotton fabric with a very soft nap. Cotton comes from the cotton plant.
12. The Romans named them Insularia Canaria (Island of Dogs) after the large breed of dogs they found there.
13. Albert when he ascended the throne, but he respected Queen Victoria's wishes that no future English king be named Albert.
14. Squirrel fur - probably named after German inventor Kemel.
15. Thirty years.
16. Sixteen; the one known as Louis XVII never reached the throne, dying in prison during the French Revolution.
17. A distinct crimson.
18. Captain Kidd was indeed hanged, but for murder. He killed one of his crew by hitting him on the head with an oaken bucket. Charges of piracy could not be proved in court.
19. Nineteen 'witches' were hanged, and one stoned to death. None were burned at the stake, nor drowned in lakes.
20. The sun is closest in our winter, which results in less radiation reaching the northern hemisphere because the sun's rays hit the earth's northern surface slant-wise and must be spread over a wider area. But when its wintertime in North America, the Earth is closer to the sun, not further away.
21. A common greeting in early England was "God rest ye merry," so the comma should follow the word merry, as in "God rest ye merry, gentlemen."
22. Reverent. Christ's name begins with X (for chi) in Greek, and as most of the early gospels were originally written in Greek, "Xmas" would refer to Christ's birth in a reverent way.

Tuesday, April 10, 2007

Book of Creation


This version of Genesis honors the Bishop of Ussher, who decreed that the Earth is not nearly as old as theorized by some, and realized that questions were being asked which created doubt about the bible itself. So adamant was the good Irish bishop that the age of the earth (and the universe) was relatively recent that he set out to pore through the bible to calculate actual ages of biblical persons and their genealogy, back to Adam and Eve. He published his findings in 1654. Apparently this Anglican prelate also claimed that he could trace his own lineage directly back to the Garden of Eden.

Remember the snake?



ONE

1 In the beginning, God created dates.

2 And the date was Sunday, October 23, 4004 B.C.

3 The very next day God said, "Let there be light," and there was light. And when there was light, God saw the date, and that it was Monday, and He got down to work; for verily, He had a Big Job to do.

4 And God made pottery shards and Silurian mollusks and pre-Cambrian Limestone strata; and flints and Jurassic mastodon tusks and Pithecanthropus erectus skulls and Cretaceous Placentalia made He; and those paintings at Lascaux. And that was that for the first workday.

5 And God saw that He had made many wondrous things but that He had not wherein to put them all. And God said, "Let the heavens be divided from the Earth; and let Us bury all of these things which We have made in the earth; but not too deep."

6 And God buried all the things which He had made, and that was that.

7 And the morning and the evening and the overtime were Tuesday.

8 And God said, "Let there be water; and let the dry land appear." And that was that.

9 And God called the dry land Real Estate; and the water He called the Sea. And in the land and beneath it He put crude oil, grades I through 6; and natural gas put He thereunder; and prehistoric carboniferous forests yielding anthracite and other ligneous matter; and all these He called Resources; and He made them abundant.

10 And likewise all that was in the sea, even unto 200 miles from dry land, called He resources; all that was therein, like manganese nodules, for instance.

11 And the morning unto the evening had been a long day, which He called Wednesday.

12. And on the fourth day, God noticed that there had been mornings and evenings, and light and darkness for the past three days;

13 But nevertheless, God said, "Let there be light in the heavens to divide day from night," and that was that.

14 And God said, "Let the water bring forth abundantly every moving creature I can think of, with or without backbones, with or without wings or fins or feet or claws, vestigial limbs and all, right now; and let each one be of a separate species. For Lo! I can make whatsoever I like, whensoever I like."

15 And the earth brought fort abundantly all creatures, great and small, with or without backbones, with or without wings and feet and fins and claws, vestigial limbs and all, from bugs to brontosauruses.

16 But God blessed them all, saying, "Be fruitful and multiply and evolve not."

17 And God looked upon the species He had made and saw that the earth was exceedingly crowded, and He said unto them, "Let each species compete for what it needeth; for Healthy Competition is My Law." And the species competed amongst themselves, the cattle and the creeping things, the dogs and the dinosaurs; some madeth it and some didn't; and the dogs ate the dinosaurs and God was pleased.

18 And God took the bones from the dinosaurs and caused them to appear mighty old; and cast them about the land and the sea. And he took every tiny creature that had not madeth it and caused them to become fossils; and cast He them about likewise.

19 And just to put matters beyond the shadow of a doubt, God then created Carbon Dating. And that is the Origin of Species.

20 And in the evening of the day which was Thursday, God saw that He had put in another good day's work.

21 And God said, "Let us make Man in Our image, after Our Likeness, which is tall and well-formed and pale of hue; and let Us also make monkeys, which resembleth Us not in any wise but are short and hairy and ill-formed." And God added, "Let man have dominion over the monkeys and the fowl of the air and every species, endangered and otherwise, and let everything that is in the earth or on it or under it or over it or near it, including but not limited to mineral rights, timber rights, drilling rights, rights of way, easements and eminent domain, without let or hinderance, irrespective of prior claim, in perpetuity, signed GOD."

22 So God created Man in His Own Image; tall and well-formed and pale of hue created He him, and nothing at all like the monkeys.

23 And God blessed him, and God said unto him, "See paragraph 21 above, passim."

24 And God said, "Behold, I have given you every herb bearing seed which is upon the surface of the earth. To you it shall be for meat. But ye shalt not smoketh it, lest it give ye ideas."

25 "And to every beast of the earth and every fowl of the air I have also given every green herb, and to them it shall be for meat. But they shalt also be meat for you. And the Lord Thy God suggesteth that the flesh of the cattle goeth well with the fin and the claw; thus shall Surf be weddeth unto Turf."

26 And God saw everything He had made, and He saw that it was very good; and God said, "It just goes to show Me what the private sector can accomplish. With a lot of fool regulations, this could have taken billions of years, foresooth."

27 And on the evening of the fifth day, which had been the roughest day yet, God said, "Thank Me it's Friday." And God thus made the week-end.

TWO

1 Thus the heavens and the earth were finished, and all in 5 days, give or take; and all less than six thousand years ago; and if thou believest it not, in a sling shalt thou find thy hindmost quarters.

2 Likewise, God took the dust of the ground and the slime of the sea and the scum of the earth and formed He Man therefrom; and He breathed the breath of life right into his face. And he became free to choose.

3 And God made a marketplace east of Eden, in which the man was free to play. And this was the free play of the marketplace.

4 And out of the ground made the Lord God to grow four trees; the Tree of Life, and the Tree of Liberty, and the Tree of the Pursuit of Happiness, and the Tree of the Knowledge of Sex.

5 And the Lord God commanded the man, saying, "This is My Law, which is called the Law of Supply and Demand. Investeth thou in the trees of Life, Liberty and the Pursuit of Hapiness, and thou shalt make for thyself a veritable fortune. For what fruit thou eateth not, thou mayest sell, and with the seeds thereof expand thy operation.

6 "But of the fruit of the Knowledge of Sex thou mayest not eat; nor mayest thou invest therein, nor profit thereby nor expand its operations; for that is a mighty waste of seed.

7 And the man was exceedingly glad. But he asketh the Lord God, "Who then shall labor in this marketplace? For am I not management, being tall and well-formed and pale of hue?"

8 And the Lord God said unto Himself, "Verily, this kid hath the potential which is Executive."

9 And out of the ground the Lord God formed every beast of the field and every fowl of the air, and brought them unto the Man to labor for him. And they labored for peanuts.

10 Then Man was again exceedingly glad. But he spake once more upon the Lord God, saying, "Lo, I am free to play in the marketplace of the Lord, and have cheap labor in abundance; but to whom shall I sell my surplus food and realize a fortune thereby?"

11 And the Lord God said unto Himself, "Verily, this is a Live One. I shall name him Adam."

12 And He caused a deep sleep to fall upon Adam and He took from him one of his ribs, which was a spare rib.

13 And the spare rib which the Lord God had taken from the man, made He woman. And He brought her unto the man Adam, saying:

14 "This is woman and she shall purchase your fruit, to eat it; and ye shall realize a fortune thereby. For man produceth and woman consumeth, wherefore she shall be called Consumer."

15 And they were both decently clad, the Man and the Woman, from the neck even unto the ankles, and they were not ashamed.


THREE

1 Now, the snake in the grass was more permissive than any beast of the field which the Lord God had made, and he said unto Woman, "Why hath thou accepted this lowly and submissive role? For art thou not human even as the man is human?"

2 And the woman said unto the snake in the grass, "The Lord God hath ordained that I am placed under the man and must do whatsoever he telleth me to do; for is he not The Man?"

3 But the snake in the grass laughed a cunning laugh, and whispered unto the woman, "Is it not right and just that thou shouldst fulfill thy potential? For art thou not comely in thy flesh, even as the man is comely in his flesh, being tall and well-formed and pale of hue?"

4 And the woman said, "Nay, I know not; for hath not the Lord God clad us decently, from the neck even unto our toes, and forbidden that we eat of the Tree of the Knowledge of Sex?"

5 But the snake in the grass said unto the woman, whispering even into her very ear, "Whatsoever feeleth good, do thou it; and believest thou me, it feeleth good. Very, very good."

6 And when the woman saw the fruit of the Tree of the Knowledge of sex, that it was firm and ripe and juicy, she plucked thereof, and sank her teeth therein, and gave also to her husband, and he likewise sank his teeth therein.

7 And the eyes of both were opened and they saw that they were not naked.

8 And the woman then loosened Adam's uppermost garment, and he likewise loosened hers; and she loosened his nethermost garment and he hers; until they were out of their garments both, and likewise of their minds.

9 And Lo! They did dance upon the grass and ground, and they did rock backward and roll forward continuously.

10 And as they did rock and roll, the serpent that was cunning did play upon a stringed instrument of music and did smite his tail upon the ground in a hypnotic rhythm; and he did sing in a voice that was like unto four voices, "She loveth you, yea, yea, yea!"

11 And they did both twist and shout, and fall into a frenzy, both the man and the woman, and lie themselves upon the ground, and commit there abominations.

12 And when they were spent from their abominations, they did take the herb bearing seed, and did roll it and smoke it, and Lo! - it gaveth them ideas, even as the Lord had said; and they were like to commit new abominations.

13 Now, the Lord God was walking in the garden in the cool of the day with His dog; and as Adam and his wife were beginning these new abominations, the Lord God did stub His Toe of His Foot upon their hindmost quarters.

14 And as the Lord God waxed wroth, and said unto Adam, "Wherefore art thou naked? And what is that thou smoketh? And why art thou not at thy work? For have I not said unto thee that it is man's work to produce, and the part of the woman to consume whatever he produceth?"

15 And Adam and his wife didst look upon each other, and didst giggle.

16 Whereupon the Lord God did wax exceeding wroth, and He said, "Hast thou eaten of the tree whereof I commanded thee that thou shouldst not eat?"

17 And Adam said, "The woman whom Thou gavest to be with me made me do it."

18 And the Lord God said unto her, "What is this that thou hast done?" And the woman said, "The snake in the grass made me do it."

19 And the snake in the grass was heard to say, "The devil made me do it."

20 And the Lord God said unto the snake in the grass, "Thou art a permissive beast; wherefore art thou cursed to crawl upon thy belly, and be made into boots and belts and handbags thereafter."

21 Unto the woman He said, "Since thou hast harkened unto the snake in the grass, which is broad of mind and permissive, henceforth let it be thy lot to be confused and scattered in thy brains, and to be plagued by demons who shalt tempt thee to become that which thou canst not be; such as a warrior, or an extinguisher of fires, or an operator of heavy machinery.

22 "And since thou hast put aside the decent clothing wherein I clad thee, hereafter no garment shall satisfy thee, and thou shalt be overcome with longings to change thy raiment every spring and fall.

23 "And above all this, since thou hast desired to taste of the fruit of the Knowledge of Sex, now let thy very body be a curse unto thee. From generation unto generation, men shall whistle and hoot after thee as thou passeth; yea, and women also."

24 And unto Adam, He said, "Woe unto thee who hast harkened not to the voice of the Lord thy God but rather to her who is thy inferior; for thou wast free to choose. Now shalt thou be banished from the marketplace and the free play thereof; neither shalt thou pluck the fruit from the trees of Life and Liberty and the Pursuit of Happiness.

25 "In the sweat of thy face shalt thou earn thy bread, and bankruptcy shalt be thy lot; and upon thy back, as a burden unto thee, thou shalt bear Big Government; for thou hast sinned."

26 And the Lord God said unto the man, "Behold, thy knowledge of sex shall be a curse upon thee and thy generations; and thy loins shall be a trial unto thee.

27 "For whensoever thou goest into a public place, then shalt thy member rise up; when thou sitteth to eat and drink among thy fellows, likewise shall it rise up; yea, even when thou standeth before the people to preach to them in My Name shall it rise up, and be a scandal unto thee, and make an unseemly lump in thy undergarments; yet when thou goest unto your wife, thy member shall wither and rise up not."

28 And then the Lord God was silent, and waxed sad, and made as if to leave them there. But He turned, and spake softly unto Adam and his wife, Eve, saying, "Knowest thou something? Mine only hope is this: that someday, ye have children who do unto thee as ye have done unto Me."

Word Nerd #1

Nothing succeeds at having students pick up a dictionary than giving them problems such as these to solve, perhaps with the hope of picking up marks for those with a solution rate of 75% or better. I only used these on Fridays, and only occasionally, as irate parents would phone me to complain that their child had his/her nose buried in a dictionary all weekend. Here is a baker's dozen.

1. Can you find at least 3 words of five letters or more, none of which contain the letters a, e, i, o or u?
2. How far do you have to count before using the letter a in spelling a number?
3. Can you, using the same five letters. spell two words that have directly opposite meanings? (Both begin with the letter u.)
4. What 7-letter word contains 8 individual words without rearrangement of any of its letters?
5. Which English word has three consecutive dotted letters in it?
6. What word, starting with a consonant, is trailed by four consecutive vowels?
7. Find the words which contain such unlikely combinations of letters as: -tomo-, -xyg-, -dhp-, -zop-, -heon-, -riju-, -xop-, and -omah-?
8. What 5-letter word contains four personal pronouns, with the letters in the correct order?
9. Make a single, common English word from the following letters: PNLLEEEESSSSS.
10. Add one vowel to the letters WTTHFL, then unscramble them to make a valid word.
11. What word is made shorter by adding a syllable to it?
12. What is the 5-letter word whose pronunciation is not changed when four of its five letters are removed?
13. Punctuate the following so that it makes perfectly good sense (use apostrophes, quotation marks, commas, full-stops, semi-colons, colons where needed): SMITH WHERE JONES HAD HAD HAD HAD HAD HAD HAD HAD HAD HAD HAD THE EXAMINERS' APPROVAL.

















Answers:
1. crypt,gypsy,lymph,myrrh,pygmy,tryst,sylph, et al
2. one thousand
3. untie,unite
4. therein
5. hijinks
6. queue
7. TOMO=automobile,XYG=oxygen,DHP=jodhpurs,ZOP=schizophrenia,
HEON=luncheon,RIJU=marijuana,XOP=saxophone,OMAH=tomahawk
8. usher
9. sleeplessness
10. twelfth
11. short
12. queue
13. Smith, where Jones had had "had had", had had "had". "Had had" had had the examiners' approval.

Abbreviations Puzzle 2

This type of puzzle is frequently solved on subsequent attempts. Don't be surprised if while doing the dishes or reading the paper, an equation you weren't even thinking about makes absolute sense. The mind is truly a wondrous thing.

1. 36 = I. in a Y.
2. 6 = W. of H. the E.
3. 212 = D. at which W. B.
4. 3 = P. for a F. G. in F.
5. 20 = Y. that R. V. W. S.
6. 101 = D.
7. 60 = S. in a M.
8. 7 = H. of R.
9. 56 = S. of the D. in I.
10. 5 = F. on the H.
11. 40 = T. (with A. B.)
12. 30 = D. H. S. A. J. and N.
13. 1 = D. at a T.
14. 10 = A. in the B. of R.
15. 435 = M. of the H. of R.
16. 7 = W. of the A. W.
17. 31 = I. C. F. at B.-R.
18. 50 = C. in a H. D.
19. 2 = T. D. (and a P. in a P. T.)
20. 4 = H. of the A.
21. 13 = C. in a S.
22. 8 = P. of S. in the E. L.
23. 20,000 = L. U. the S.
24. 9 = I. in a B. G.







Answers
Think I'll let you ponder these a while longer... email if desperation sets in.

Monday, April 9, 2007

Paradoxia

Ten weary, footsore travelers
All in a woeful plight
Sought shelter at a wayside inn
One dark and stormy night.

"Nine rooms, no more," the landlord said
"Have I to offer you.
To each of eight a single bed,
But the ninth must serve for two."

A din arose. The troubled host
Could only scratch his head,
For of those tired men no two
Would occupy one bed.

The puzzled host was soon at ease -
He was a clever man -
And so to please his guests devised
This most ingenious plan.

In a room marked A two men were placed
The third was placed in B,
The fourth to C was then assigned
The fifth retired to D.

In E the sixth he tucked away,
In F the seventh man,
The eighth and ninth in G and H
And then to A he ran.

Wherein the host, as I have said
Had laid two travelers by;
Then taking one - the tenth and last -
He lodged him safe in I.

Nine single rooms - a room for each -
Were made to serve for ten
And this it is that puzzles me
And many wiser men.


Epilogue #1:
I had not heard the din that night
As number ten raised hue and cry
"Twas number two - not number ten -
That bedded down in room marked I.

Epilogue #2:
If we reflect on what he's done
We'll see we're not insane
Two men in A, he's counted one,
Not once, but once again.

Palindromes

As we all know, palindromes are words or preferably phrases, which read the same forwards as well as backwards. Here's a small collection:

1. Madam, I'm Adam.

2. Able was I ere I saw Elba. (Reportedly said by Napoleon as he was rowed to exile on Elba.)

3. A man, a plan, a canal: Panama.

4. Doc note, I dissent. A fast never prevents a fatness. I diet on cod.

5. Lewd did I live & evil I did dwel.

6. He goddam mad dog, eh?

7. Naomi, sex at noon taxes, I moan.

8. Step on no pets. (Sign in a vet's office)

9. Never odd or even.

10. Sit on a potato pan, Otis.

11. May a moody baby doom a yam?

12. A dum reb was I ere I saw Bermuda.

13. Am a Jap pajama.

14. Was it a cat I saw?

15. Draw pupil's lip upward.

16. Egad! A base tone denotes a bad age.


Student Reports #2

Actual student answers on science and math tests in the USA.

25. Vegetative propagation is the process by which one individual manufactures another individual by accident.
26. A super-saturated solution is one that holds more than it can hold.
27. A triangle which has an angle of 135 degrees is called an obscene triangle.
28. Blood flows down one leg and up the other.
29. A person should take a bath once in the summer, and not quite so often in the winter.
30. The hookworm larvae enter the human body through the soul.
31. When you haven't got enough iodine in your blood you get a glacier.
32. It is a well-known fact that a deceased body harms the mind.
33. Humans are more intelligent than beasts because the human branes have more convulsions.
34. For fainting: rub the person's chest, or if a lady, rub her arm above the hand instead.
35. For fractures: to see if the limb is broken, wiggle it gently back and forth.
36. For dog bite: put the dog away for several days. If he has not recovered, then kill it.
37. For nosebleed: put the nose much lower than the body.
38. For drowning: climb on top of the person and move up and down to make artificial perspiration.
39. To remove dust from the eye, pull the eye down over the nose.
40. For head colds: use an agonizer to spray the nose until it drops in your throat.
41. For snakebites: bleed the wound and rape the victim in a blanket for shock.
42. For asphyxiation: apply artificial respiration until the patient is dead.
43. Before giving a blood transfusion, find out if the blood is affirmative or negative.
44. Bar magnets have north and south poles. Horseshoe magnets have east and west poles.
45. When water freezes you can walk on it. That is what Christ did long ago in wintertime.
46. When you smell an odorless gas, it is probably carbon monoxide.
47. Equator: A managerie lion running around the Earth through Africa.
48. A fossil is an extinct animal. The older it is, the more extinct it is.
49. Water is composed of two gins, Oxygin and Hydrogin. Oxygin is pure gin. Hydrogin is gin and water.
50. When you breathe, you inspire. When you do not breathe, you expire.

Student Reports #1

Actual excerpts from science students in the USA.

1. Charles Darwin was a naturalist who wrote the Organ of the Species.
2. Benjamin Franklin produced electricity by rubbing cats backwards.
3. The theory of evolution was greatly objected to because it made man think.
4. Three kinds of blood vessels are arteries, vanes and caterpillars.
5. The dodo is a bird that is almost decent by now.
6. To remove air from a flask, fill it with water, tip the water out, and put the cork back in quick before the air can back in.
7. A magnet is something you find crawling all over a dead cat.
8. The Earth makes one resolution every 24 hours.
9. The cuckoo bird does not lay his own eggs.
10. To prevent conception when having intercourse, the male wears a condominium.
11. To collect fumes of sulfur, hold a deacon over a flame in a test tube.
12. Parallel lines never meet, unless you bend one or both of them.
13. Algebraic symbols are used when you don't know what you are talking about.
14. Geometry teaches us to bisex angles.
15. A circle is a line which meets its other end without ending.
16. The pistol of a flower is its only protection against insects.
17. The moon is a planet just like the Earth, only it is even deader.
18. Artificial insemination is when the farmer does it to the cow instead of the bull.
19. An example of animal breeding is the farmer who mated the bull that gave a great deal of milk with a bull with good meat.
20. We believe that the reptiles came from the amphibians by spontaneous generation and the study of rocks.
21. English sparrows and starlings eat the farmer's grain and soil his corpse.
22. By self-pollination, the farmer may get a flock of long-haired sheep.
23. If conditions are not favorable, bacteria go into a period of adolescence.
24. Dew is formed on leaves when the sun shines down on them and makes them perspire.

Bumper Snickers #3

It's been lovely. I have to scream now.

It's as bad as you think & they are out to get you.

Sex on television can't hurt you unless you fall off.

Is there life before coffee?

Never play leapfrog with a unicorn.

Nobody's ugly after 3 AM.

The weather is fine. Wish you were beautiful.

Smile. It's the 2nd best thing you can do with your lips.

If money could talk, it would say goodbye.

Wink. I'll do the rest.

Crime wouldn't pay if the government ran it.

The worst day fishing is better than the best day working.

Jesus loves you. Everyone else thinks you're an ass.

Impotence - Nature's way of saying "No Hard Feelings."

The proctologist called - they found your head.

Everyone has a photographic memory. Some just don't have any film.

Wanted: Meaningful overnight relationship.

Guys: just because you have one, doesn't mean you have to be one.

Heart Attacks are God's revenge for eatinh His animal friends.

Bumper Snickers #2

All the following were collected within New York City:

Forget about World Peace... Visualize Using Your Turn Signal.

We are born naked, wet & hungry. Then things get worse.

Make it idiot proof & along comes a better idiot.

Lottery: a tax on people who suck at math.

Consciousness: that annoying time between naps.

Diplomacy: the art of saying "Nice doggie" until you can find a big enough rock.

I'm a corporate executive. I keep things from happening.

I love cats. They taste a bit like chicken.

The gene pool could use a bit more chlorine.

I didn't fight my way to the top of the food chain to be a vegetarian.

Bumper Snickers #1

Some randomly seen bumper stickers from around the world:

Auntie Em. Hate you, hate Kansas, taking the dog. Dorothy.

My karma ran over your dogma.

Women who seek to be equal to men lack ambition.

Life's too short to dance with ugly women.

I is a college graduat.

Beer isn't just for breakfast anymore.

Sorry, I don't date outside my species.

Eschew obfuscation.

Will Rogers never met a lawyer.

It's lonely at the top but you eat better.

Don't steal. The government hates competition.

Cover me. I'm changing lanes.

Jeez if you believe honkus.

I came, I saw, I did a little shopping.

Just when you think you've won the rat race, along come faster rats.

Jesus is Coming. Look busy.

Aptitude Test

1. If you went to sleep at 8 o'clock at night, having set the wind-up alarm clock to ring at 9 o'clock in the morning, how many hours of sleep would you get?

2. Do they have a First of July in England?

3. How many birthdays does the typical North American man have?

4. Why can't the man living in Winston-Salem, North Carolina, be legally buried west of the Mississippi River?

5. If you only had one wooden match and entered a cabin in which there were three items: a kerosene lamp, an oil heater and a wood-burning stove, which would you light first?

6. Some months have 30 days, some 31. How many months have 28 days?

7. A man built his house with four sides and square in shape. The funny thing about the house was that each side had a southern exposure. A big bear came wandering by. What color was the bear?

8. How far can a dog run into the woods?

9. I hold in my hand two Canadian coins which total 30 cents in value. One is NOT a quarter. Bearing this fact in mind, what are the two coins?

10. A farmer had 17 sheep. All but nine died. How many sheep did the farmer have left?

11. Take two apples from three apples and what do you have?

12. An archaeologist claimed that he found some ancient coins that were inscribed with 400 B.C. and that this proved that they were authentic. Do you believe he was right?

13. How many animals of each species did Moses take aboard the ark with him?

14. Is it legal in Quebec for a man to marry his widow's sister?

15. A woman gives a beggar fifty cents. The woman is the beggar's sister, but the beggar is NOT the woman's brother. Explain how this could be possible.

16. If a British airliner crashed exactly on the border between Canada and the USA, where would they bury the survivors?

17. How can 5 people divide a sack of five apples equally, without cutting them up, and still have one apple remaining in the sack?

18. A secretary types 4 letters, then 4 envelopes which she addresses to 4 different people. She inserts the letters at random, not matching the correct letter to the right envelope. Calculate the probability that exactly THREE of the letters will be inserted in the correct envelopes.

19. Divide 30 by 1/2 and add 10. What is your answer?

20. How many times can one subtract the numeral one from the numeral twenty-five?




ANSWERS
1. One hour
2. Yes, they have a first of July everywhere
3. One only - the rest are anniversaries
4. Because he's still alive
5. The match, dummy
6. They all do
7. White - or rather, polar bears are an off-white
8. Exactly half-way; after that, it will be running OUT of the woods
9. The OTHER coin was the quarter
10. Nine, of course. The others are dead.
11. Two
12. The symbols BC came about after the birth of Christ (anno domini or AD)
13. Moses was never on the ark - it was Noah
14. It's illegal for a dead person to marry anyone, anywhere in Canada
15. The beggar is a woman
16. Assumedly, they would bury the survivors whenever and wherever they died
17. The last person got the last apple when it was still in the sack
18. None: if three are in the right envelopes, the last one must also be in the right envelope
19. Seventy
20. Once. After that, you will be subtracting from the numeral 24, then 23, and so on



Proverbs that didn't make it

All of the following have a relationship to well-known proverbs, but for one reason or another did not make the grade. Nonetheless, we feel they are perhaps superior to their better-known cousins.

A rolling stone gets the worm.

A bird in the hand waits for no man.

The road to hell has a silver lining.

It's an ill wind that spoils the broth.

There's no fuel like an oil fuel.

There's no police like Holmes.

People who live in glass houses shouldn't.

All work and no play makes jack.

Familiarity breeds.

When all else fails, read the instructions.

The chief cause of problems is solutions.

Common sense is the least common of all senses.

A bird in the hand - may pee.

You can't tell a book by its movie.

A man without a religion is like a fish without a bicycle.


Peas On Earth

In the beginning there was Mendel, thinking his lonely thoughts alone. And he said, "Let there be peas," and there were peas, and it was good. And he put the peas in the garden, saying unto them, "Increase and multiply, segregate and assort yourselves independently," and they did, and it was good.

Now it came to pass that when Mendel gathered up his peas, he divided them into round and wrinkled, and called the round dominant and the wrinkled recessive, and it was good. But now Mendel saw that there were 450 round peas and 102 wrinkled ones; this was not good, for the Law stateth that there should be only 3 round for every one wrinkled. And Mendel said unto himself, "Gott in himmel, an enemy hath done this: he hath sown bad peas in my garden under the cover of night."

And Mendel smote the table in righteous wrath, saying, "Depart from me, ye cursed and evil peas, into the outer and nether darkness where thou shalt be devoured by rats and mice," and Lo! it was done, and there remained 300 round peas and 100 wrinkled, and it was good. It was very, very, very good. And Mendel published.


-excerpted from 'Horticultural Science'

Calculate or Guess #1

Some very curious problems - by I. Akulich

Problem 1.
A father is 26 years old and his son is 6 years old. In how many years will the father be three times as old as his son?

This problem and others like it are usually solved by one of two methods.
Arithmetic Method: If the father becomes three times older than his son, the difference in their ages is two times the son's age. But the difference is constant and is equal to 26 - 6 = 20 years, so the son's age at the moment we're looking for will equal 20 / 2 = 10 years, which will happen in 10 - 6 = 4 years.
Algebraic Method: Let the father be three times older than his son in x years. Then
26 + x = 3( 6 + x ), so x = 4.

Let's add one more method to these two - the Guess-and-Choose Method. Let's try to guess the answer, or more exactly, to choose it. Let's use our experience in solving such problems and remember that, as a rule, only integers are used in them. The search area then becomes sharply delimited. In addition, when the father becomes three times as old as the son, naturally his age must be divisible by three. At first this situation will happen in a year - that is, the father will be 27 and the son 7 (which doesn't work); then in 4 years - that is, the father will be 30 and his son 10 (now it does work). So that's it!

If any of you is thinking of indignantly rejecting this method in favor of the first two, I strongly urge you to hold off. It's true. a mathematician (even an amateur one) ought not to guess. But imagine the following situation. A math competition is taking place. One participant from each team is called upon to solve the above problem. The first to give the correct answer is declared the winner. And so the clock starts ticking! You can't help but agree that the third method seems preferable to the first two. Of course, there's the chance of not finding the answer at all, but the greater speed and more limited number of calculations (and consequently, the greatly reduced possibility of making arithmetical errors, which are quite likely in the heat of competition) are sure to outweigh that consideration.


Problem 2.
According to legend there was a tombstone with this inscription: "Ye traveller, lying under this tombstone are the remains of Diophantos, who died in extreme old age. He was a child for a sixth of his long life, a youth for a twelfth, and unmarried for a seventh. Five years after he was married his wife had a baby boy, who lived half as long as his father. Four years after his son's death Diophantos himself went to his eternal rest, and his death is mourned by his relatives. Tell me if you can count, how many years Diophantos lived."

If you use the algebraic method, you have to solve a cumbersome equation, and the arithmetic solution isn't any simpler. What about the guessing method? Let's think about it this way - since all the numbers must very likely be integers, the number of years that Diophantos lived must divide evenly by 6, by 12, and by 7 - that is, by their least common multiple, which equals 84. This means that the number of years lived by Diophantos is a multiple of 84 - in fact is 84. (Larger numbers would be unrealistic.) So that's it!

In this specific example, the advantages of the guessing method become really obvious.


Problem 3.
One day the devil proposed to a certain goof-off that he earn some money. "As soon as you cross the bridge," he said, "your money will double. You may cross the bridge as many times as you like, but every time you do you must pay me 24 cents." The goof-off agreed - and after the third crossing he was penniless. How much money did he start off with?

Let's try to guess the answer, using general reasoning. It's clear that the goof-off had less than 24 cents at the start, otherwise he wouldn't have gone bankrupt. In other words, from the very beginning there was a 'budget deficit.' Money doubling was apparently accompanied by a deficit doubling, and after the third crossing the doubled deficit amounted to exactly 24 cents. This means that at first the deficit was equal to 24 / 2^3 = 3 cents - that is, the goof-off had 24 - 3 = 21 cents in his pockets to begin. Of course, we cannot guarantee that this answer is right, but it's certainly very plausible.


Problem 4. (with thanks to America's best puzzlist, Sam Loyd)
"Here are two turkeys," the butcher says, "one tom and one hen. Together they weigh 20 pounds. But the price per pound of the hen is two cents higher than the price per pound of the tom." Mrs. Smith bought a turkey hen and paid 82 cents for it, while a Mrs. Brown paid $2.96 for the tom turkey. (NOTE: Sam Loyd lived from 1841 to 1911) What did each turkey weigh?

Let's take some risks: suppose each turkey weighed an integral number of pounds and the price per pound is an integral number of cents. The total sum paid was 378 cents. If the extra charge for the hen's meat is subtracted from the total, the remainder must divide by 20, which is the total weight of the turkeys. The nearest least number divisible by 20 is 360 - that is, the extra charge is equal to 18 cents, so the tom weighed 11 pounds.

We have an answer, but the hen turned out to be a bit hefty, didn't it? The difference in weights is quite small, but the price of the hen is one-fourth that of the tom, even though the price per pound of the hen is higher. Something's wrong!

Sure enough, this is a case where our guessing method misfires. We made a faulty assumption and so we're doomed to failure. We had no way of knowing that this is a historical problem beside my warning above, but should now realize that as late as the 40's many grocery items were priced to the half-cent. Armed with this knowledge, try to guesstimate the answer.

Sunday, April 8, 2007

NIM

I was first introduced to this wonderful game when I saw an old black & white film called "Last Year at Marienbad" (if memory serves right), in which two students whiled away the hours at a cafe playing this game with matchsticks. When Martin Gardner wrote an analysis of the game, and revealed the elegant solution in his Scientific American column, I decided that it would be an excellent tool in a math teacher's toolbox to introduce binary notation.

The game can be played with pencils & paper, toothpicks or matches on a table, or coins. The basic idea is that two players alternate removing one, or more matches, from any number of matches in three rows, until the winner has the option of removing the last match or matches in any one row.

This can most easily be shown as follows: Assume three rows consisting of one match in row one, two matches in row two, and three matches in row three.
I
I I
I I I
Player A goes first, and has the option of removing one, or more, matches from any one row. Now, what he doesn't know is that by going first, he automatically will lose, for that is the fate ordained for him by mathematics. Let's assume he removes one match from row three, leaving the following tableau for player B.
I
I I
I I
All player B has to do is remove the one match from row one, and he can't fail but win. If he does so, he will leave behind two rows of two matches each:
I I
I I
Player A has to go next, and if he were to remove BOTH matches from one row, the winner would be player B, as he could remove BOTH matches in the remaining row. Remember, the winner is the player who gets to remove one, or more matches from the last row.
If player A removed just ONE match from either row, player B would still win by removing ONE match from the OTHER row, leaving one match in each row. As player A had to go next, and could only remove a match from one row, he'd leave the last match for the winner, player B.

So what is the secret to the game? How can one make it truly challenging & fun to play?

There is a winning strategy, and it involves binary notation, which you must learn to win at this game consistently. If there's one match in a row, it would be represented by 0001; if there were two matches in a row, it would be represented binarily as 0010; three would be written 0011; and eight would be 1000.

In our game illustrated, consisting of one, two & three matches, row one would be 0001, row two would be 0010, and row three 0011. If we add up those binary digits, we'd get a sum of 0022.
The secret is to make the binary sums even for your opponent, and force him to make it add up odd for your turn. That's assuming there are three rows, containing at least one match each, and you can't lose. Of course, should your opponent manage to take the match or matches from a whole row, your task is to make the binary sums even, and you can't lose.

This all takes a little practice, and of course the fun is to have a reasonable number of matches in each row to make the game last longer, and more thought-provoking. Take this example of three rows of 5, 7, and 8 matches. Converted to binary notation, you have 0101, 0111 and 1000 which adds up to 1212. If it's your turn to go, and it better be your turn as it's not a winning strategy as it stands, you can only win by removing all but two matches from row three, because that makes the sum then add up to all even numbers: 0101, 0111 and 0010 will add up to 0222. Your opponent can't win, just prolong the agony.

I used to show the class how the game is played with 1, 2 & 3 matches, and progress to 3, 4 & 5.
In order to make the game fair for both players, I instituted this rule: the person who decides on the number of matches in the 3 rows has to wait for his opponent to decide who goes first. If the student was wise to the method, and wanted me to decide on the number of matches, I'd use larger numbers to start with, in the hope that they wouldn't add up the binary sums properly, and I would gain the winning strategy when they made an error and removed the wrong number of matches.

Naturally, the students who became proficient at NIM got quite good at the binary numeration system, and succeeded in the other non-decimal systems as well.

Abbreviations Puzzle 1

In the few years since this little test was introduced, it has been found that very few people solve more than five or six of the two dozen questions at the first try.

Instructions: Each question contains the initials of words that will make it correct; your task is to find the missing words.
Example: 16 = O. in a P. (16 = Ounces in a Pound)

1. 26 = L. of the A.
2. 7 = D. of the W.
3. 1001 = A. N.
4. 12 = S. of the Z.
5. 54 = C. in the D. (including the J.)
6. 9 = P. in the S. S.
7. 88 = P. K.
8. 13 = S. on the A. F.
9. 32 = D. F. at which W. F.
10. 18 = H. on a G. C.
11. 90 = D. in a R. A.
12. 200 = D. for P. G. in M.
13. 8 = S. on a S. S.
14. 3 = B. M. (S. H. T. R.)
15. 4 = Q. in a G.
16. 24 = H. in a D.
17. 1 = W. on a U.
18. 5 = D. in a Z. C.
19. 57 = H. V.
20. 11 = P. on a F. T.
21. 1000 = W. that a P. is W.
22. 29 = D. in F. in a L. Y.
23. 64 = S. on a C. B.
24. 40 = D. and N. of the G. F.








Answers:
1. Letters, alphabet
2. Days, week
3. Arabian, nights
4. Signs, zodiac
5. Cards, deck(jokers)
6. Planets, solar, system
7. Piano, keys
8. Stripes, American, flag
9. Degrees, Fahrenheit, water, freezes
10. Holes, golf, course
11. Degrees, right, angle
12. Dollars, passing, go, monopoly
13. Sides, stop, sign
14. Blind, mice, see,how, they, run
15. Quarts, gallon
16. Hours, day
17. Wheels, unicycle
18. Digits, zip, code
19. Heinz, varieties
20. Players, football, team
21. Words, picture, worth
22. Days, February, leap, year
23. Squares, chess, board
24. Days, nights, great, flood