Taken From "DISCOVER" and "SCIENCE DIGEST" 1 Given 5 blue and 5 red dots in a plane, no three colinear, prove that it is possible to contruct five line segments starting at a red dot and terminating at a blue dot such that no two of these five line segments intersect each other. 2 Use the following primes and construct a magic sqaure. Hint: The magic sum of this square is called the "number of the beast". [666] 003 005 007 011 013 017 031 037 041 047 053 059 061 071 073 083 089 097 101 103 107 109 113 127 131 139 151 167 173 179 193 197 199 311 331 387 3 Ten fish I caught without an eye, And nine without a tail, Six had no head, and half of eight I weighed upon the scale; No one who can tell me as I ask it, How many fish were there in my basket? [0] 4 He went to the wood and caught it, He sate him down and sought it; Because he could not find it, Home with him he brought it. [thorn] 5 Because I am by nature blind, I wisely choose to walk behind; However, to avoid disgrace, I let no creature see my face. My words are few, but spoke with sense; And yet my speaking gives offence: Or if to whisper I presume The company will fly the room. By all the world I am opprest; And my oppression gives them rest. [the posterior] 6 The noblest object in the works of art, The brightest scenes which nature can impart; The well known signal in the time of peace, The point essential in a tennant's lease; The farmers comfort as he drives the plough, A soldier's duty and a lover's vow; A contract made before the nuptial tie, A blessing riches can never supply; A spot that adds new charms to pretty faces, An engine used in fundamental cases; A planet seen between the earth and sun, A prize that merit never yet has won; A loss which prudence can seldom retreive, The death of Judas, and the fall of Eve; A part between the ankle and the knee, A papist's toast, and a physician's fee; A wife's ambition and a parson's dues, A miser's idol, and the badge of Jews. If now your happy genius can divine The correspondent words in every line, By the first letter plainly may be found An ancient city that is much renowned. 7 I sit alone on a rock Whils't I am raising a wind, But the storm once abated I'm gentle and kind. I have kings at my feet Who await but my nod, To kneel doen in the deep, On the ground that I have trod. Tho' oft seen by the world, I am known but to few; The gentiles despise me, I'm pork to the Jew. I never have passed But one night in the dark, And that was with Noah Alone in the Ark. My weight is three pounds, My length is a mile; And when I am discovered You will say with a smile That my first and my last Are the best of our isle. 8 I'm found in most countries, yet not in earh or sea, I am in all timber and yet not in any tree, I am in all metals, yet I am told, I am not in lead, iron, brass, silver or gold, I am not in England, yet this I can say, I'm to be found in Westminster every day. ["M"] 9 Of a brave set of brethren I stand at the head, Ans to keep them quite warm, I cram three in a bed; Six of them in prison unfeelingly put, And three I confine in a mean little hut; To escape my fell gripe, three reside in the sky; And though strange it may seem, we have all but one eye; Our shape is as various as wondrous our use is, Of Science the source, and the soul of the muses. ["A"] 10 Expand MALE [Merely A Lady's Escort] 11 {This problem was proposed by Archimedes about 2200 years ago and was solved only recently that too not by a human} Compute, O friend the host of oxen of the sun, giving thy mind thereto, if thou hast a share of wisdom. Compute the number that once grazed upon the plains of the Sicilian isle Trinacria (Sicily itself) and that were divided according to color into four herds, one milk-white, one black, one yellow and one dappled. The number of bulls formed the majority in each herd and the relations between them were: 1. White bulls = yellow bulls + (1/2 + 1/3) black bulls 2. Black bulls = yellow bulls + (1/4 + 1/5) dappled bulls 3. Dappled bulls = yellow bulls + (1/6 + 1/7) white bulls 4. White cows = (1/3 + 1/4) black herd 5. Black cows = (1/4 + 1/5) dappled herd 6. Dappled cows = (1/5 + 1/6) yellow herd 7. Yellow cows = (1/6 + 1/7) white herd If thou canst give O friend the number of bulls and cows in each herd, thou art not all knowing nor unskilled in number, but not yet to be counted among the wise. Consider however the additional relations between the bulls of the sun: 8. White bulls + Black bulls = triangular number 9. Dappled bulls + yellow bulls = square number. When thou hast then computed the totals of the herd, O friend go forth as the conqueror, and rest assured that thou art proved most skilled in the science of numbers. [The smallest composite herd satisying the first 7 conditions was found to be 50,389,082 cattle. A German investigator proved that the final solution is a 206,545 digit number starting with 7766. Later using a super computer it was found that there were five additional solutions the largest containing more than a million digits.] 12 Interesting Palindromes "I SAW I WAS DNA AND SAW I WAS I." {One side of a telephone conversation} "NO! ... TOO BAD! ... AH! I WAS NEVER EVER EVEN TIRED! ... NOW, IS EIRE VERY SORDID? ... OH! WON'T I? ... DID I? ... WAS I NOT UP SPOT ON? ... I SAW NO SHELL? ... I SAW IT! ... I DID! I? ... FIRED? ... NO WONDER! ... IT SAW DAD WAS WELL LEFT ... I SAT RAPT! ... I DID? ... WON'T I? ... NO! ... RED? ... NO! ... PREVENT iT? ... NEVER! ... PONDER ON IT NOW! ... DID IT PART AS IT FELL? LEW SAW DAD WAS TIRED ... NO WONDER, IF I DID IT? ... I WAS ILL, EH SON? ... WAS I? ... NO TOPS PUT ON, I SAW ... I DID IT? ... NO ... WHO DID? ... ROSY REVERIES? I WONDER! ... IT NEVER EVEN SAW I HAD A BOOT ON!"