LITTONS PROBLEMATIC RECREATION

2 A thoroughly inbred family-the physicist not only married his cousin, but so did his brother and his sister-resulting in a party of two, including the host.

A Solid State Physicist gives a small stag party. He invites his father's brother-in-law, his brother's father-in-law, his father-in- law's brother, and his brother-in-law's father. Find the number of guests" 2 5 10 12

3, 3, and 2 bricks

A bricklayer has 8 bricks. Seven of the bricks weigh the same amount and 1 is a little heavier than the others. If the man has a balance scale how can he find the heaviest brick in only 2 weighings? 3-3-2 2-4-2 3-4-1 2-5-1

dropping a penny into the canoe will raise the water level higher. It does make a difference. A submerged body displaces its volume; a floating body displaces its weight. Since a penny is denser than water, dropping it into the canoe will raise the water level higher.

A canoe is floating in a swimming pool. Which will raise the level of the water in the pool higher, dropping a penny into the pool or into the canoe? Or does it make any difference ? dropping a penny into the canoe will raise the water level higher. dropping a penny into the pool will raise the water level higher. dropping a penny into the canoe or pool will not raise the water level higher. dropping a penny into the canoe or pool would result in the same rise in water level.

0.618

A coin is so unbalanced that you are likely to get two heads in two successive throws as you are to get tails in one. What is the probability of getting heads in a single throw?

President - Mr. White Professor - Mr. Brown Instructor - Mr. Black Janitor - Mr. Green Seven-year-olds don't have wives in Philadelphia, fathers rarely confuse their children's names ... this kind of logic plus a little digging reveals that Mr. White is the president, Mr. Brown is the professor, Mr. Black is the instructor and Mr. Green is the Janitor.

A college president, a professor, an instructor, and a janitor are named Mr. Brown, Mr. Green, Mr. White, and Mr. Black, but not respectively. Four students with the same names will be designated here as Brown, Green, White and Black. The student with the same name as the professor belongs to Black's fraternity. Mr. Green's daughter-in-law lives in Philadelphia. The father of one of the students always confuses White and Green in class, but is not absent- minded. The janitor's wife has never seen Mr. Black. Mr. White is the instructor's father-in-law and has no grandchildren. The president's oldest son is seven. What are the names of the president, professor, instructor, and janitor? Answer President - Mr. White Professor - Mr. Brown Instructor - Mr. Black Janitor - Mr. Green

lose

A gambler devised a game to be played with a friend. He bet 1/2 the money in his pocket on the toss of a coin; heads he won, tails he lost. The coin was tossed and the money handed over. The offer was repeated and the game continued. Each time the bet was for 1/2 the money then in his possession. Eventually the number of times he lost was equal to the number of times he won. Quickly now! Did he gain, lose, or break even? Gain Lose Break Even

196 There are altogether 7^3 or 343 possibilities. Of these, 49 read the same backward or forward. Half the remaining 294 must be eliminated since they are duplicates. There are, therefore, a total of 196 pieces in the set.

A game of super-dominoes is played with pieces divided into three cells instead of the usual two, containing all combinations from triple blank to triple six, with no duplications. For example the set does not include both 1 2 3 and 3 2 1 since these are merely reversals of each other. (But, it does contain 1 3 2.) How many pieces are there in a set? 196 201 251 260

Smith should leave two chains of 6 and 3 links. If Jones leaves 1, 1, 1, 4 or 1, 1,2,3, Smith can leave 1, 2; if Jones leaves 1, 2, 4 or 2, 2, 3, Smith can leave 1, 1, 2, and if Jones leaves 2, 5 or 1, 1, 5, Smith can leave 1, 2, 2 or 1, 1, 2, respectively, in all cases winning on the next move.

A game proceeds as follows: Smith starts with a l0-link chain and removes any single link, presenting Jones either with a 9-link chain or two chains having a total of 9 links. Jones removes any one link from each of the chains. Smith removes any one link from each of the remaining chains and so on, until the winner removes the last link or links. What should Smith do first? Smith should leave two chains of 6 and 3 links.

2/5

A hospital nursery contains only two baby boys; the girls have not yet been counted. At 2:00 p.m. a new baby is added to the nursery. A baby is then selected at random to be the first to have its footprint taken. It turns out to be a boy. What is the probability that the Iast addition to the nursery was a girl? 2/5 3/5 2/3 1/2

He could put his gun diagonally in a cubical box, 1 yard on a side

A hunter wished to take his one-piece rifle on a train but the conductor refused to permit it in the coach and the baggage man could not take any article whose greatest dimension exceeded I yard. The length of the rifle was 1.7 yards' What could the hunter do? He could put his gun diagonally in a cubical box, 1 yard on a side He could put his gun horizontally in a cubical box, 1 yard on a side He could put his gun vertically in a cubical box, 1 yard on a side

99 This number holds true regardless of the manner in which the ptzile is assembled. The proof is trivial. We start with 10O pieces and end up with a single cluster. Each move reduces the total number of clusters by one. Hence 99 mov€S.

A jig-saw puzzle contains 100 pieces. A "move" cdosists of connecting two clusters (including "clusters" of just one piece.) What is the minimum number of moves required to complete the puzzle? 98 99 100 101

1/6. Both lights are red during the 1st and l2th seconds and never match at any other time. The answer, therefore, is 1/6.

A lighthouse shows successive one-second flashes of red, white, green, green, white, red. A second lighthouse does the same only with two-second flashes. The six-second sequence of the first lighthouse is repeated steadily, as is the twelve-second sequence of the other lighthouse. What fraction of the time do the two lights show the same color if the given sequences start at the same time? 1/3 1/6 1/12 1/24

The statements cannot all be false

A list contains 1968 statements, numbered in serial order' For each k, the kth statement is: "This list contains exactly k false statements." Determine the truth or falsity of each statement! The statements cannot all be false

0.168

A long shot poker player draws two cards to the five and six of diamonds and the joker. What are his chances of coming up with a pat hand? (straight or flush). 0.132 0.168 0.211 0.315

R G R B R G R. He now cannot use R for then there would be two consecutive R's. He cannot use G' because there would be two consecutive R G's. He cannot use B for then there would be two consecutive R G R B's. Any other pattern for the first seven stones would have allowed a choice for the eighth not involving a repetition.

A man has red, gray and black flagstones for making a walk- He wants no two consecutive stones to be the same color, no consecutive pair of stones to have the same two colors in the same order, no repetition of three consecutive colors' etc. He starts out laying first a red stone, then a gray, and continues until he finishes laying the seventh stone. He then finds himself stymied and unable to use any stone for the eighth without repetition of some color pattern. What were the colors of the first seven stones?* R G R B R G R.

infinity The journey can be completed by starting it at an infinity of points. One such point is the north pole; all others lie in the neighborhood of the south pole and require one or more complete westward trips about the pole.

A man walks one mile south, one mile west, then one mile north, ending where he began. From how many points on the surface of the earth can such a journey be made? (there are more than 1)? one mile one million impossible infinity

15 He must pick up 7 shirts to tide him over until the following Monday. Ilence he must deposit 7 shirts each Monday. Countl ing the shirt he wears on Monday, the required toiut i. t5. (Note that he cannot get by with only 14 by exchanging his Monday shirt for a clean one and turning it in to tfre iaridry as he will be caught short the following Monday.)

A neat computer programmer wears a clean shirt every day. If he drops off his laundry and picks up the previous week's load every Monday night, how many shirts must he own to keep him going? 7 8 14 15

Between volumes 10 and 3. Evidently the librarian is shelving according to the alphabetical order of the volume numbers.

A novice librarian shelved a twelve-volume set of encyclopedias in the following order from left to right. Volumes 8, 11, 5, 4, 9, 1, 7, 6, 10, 3, 12, and 2. Using her system, where will the annual supplement, Volume 13, go? Between volumes 11 and 3 Between volumes 10 and 3 Between volumes 9 and 4 Between volumes 9 and 3

1 white on one box and 9 whites and 10 blacks on the other box If the prisoner places one white ball in one box and the remaining balls (9 white and 10 black) in the other box, his chance of survival would be (1 + 9/19)/2 = 0.737, or 73.7%.

A prisoner is given 10 white balls, 10 black balls and two boxes. He is told that an executioner will draw one ball from one of the two boxes. If it is white, the prisoner will go free; if it is black, he will die. How should the prisoner arrange the balls in the boxes to give himself the best chance for survival? 5 white and 5 blacks on each box 1 white on one box and 9 whites and 10 blacks on the other box 10 whites on one box and 10 blacks on the other box 9 blacks and 1 white in one box and 1 black and 9 white on the other

first wife's lone remaining child The 2nd wife underestimated her husband. She knew the first 14 eliminations would occur at positions 3,7,8,9, 10, 11, 15, 20, 22, 23, 24,26, 27, and 30, but he knew the first counted out of 16 would survive 15 eliminations.

A rich farmer had 15 children by his first wife and 15 by his second. The second wife wished to insure the heritage to one of her own children and persuaded him to seat all 30 in a circle and count off every tenth child until only 1 remained. The first 14 thus eliminated were all his first wife's children. From this point on he insisted that they count backward from his first wife's lone remaining child. In what order were his first wife's children? Who became heir? first wife's lone remaining child one of the second's wife's children Farmer didn't choose an heir Cannot say

83

A salesman visits ten cities arranged in the form of a circle, spending a day in each. He proceeds clockwise from one city to the next, except whenever leaving the tenth city he may go to either the first or jump to the second city. How many days must elapse before his location is completely indeterminate, i.e., when he could be in any one of the ten cities? 80 81 82 83

NEARBY, WALRUS, ASYLUM RB. can only be NEARBY and .. .LR ... must be WALRUS. Then we can convert KVJZDC into ASYLU., which is obviously ASYLUM. FWF JID EQO WO?

A simple substitution cipher message was worked out on a blackboard and accidentally erased. A few fragments remain, however. The word G Q K X Y J has escaped erasure with X identified as R and Y as B. Also the word P K Z X D V can be made out with Z identified as L. The only other legible word is K V J ZD C. What word does this represent?

Mother

A teenager wants to go out 2 consecutive nights out of a 3-day weekend. Permission for each night is obtained (or denied) by asking either Father or Mother. Father is known to be more likely to grant permission. However, if the same parent is asked on 2 consecutive days the answers are never the same 2 days running. Whom should he ask first? Father Mother Both None

The fraternity had 15 members and could field 3,003 teams of either type

All the members of a fraternity play basketball while all but one play ice hockey; yet the number of possible basketball teams (5 members) is the same as the number of possible ice hockey teams (6 members). Assuming there are enough members to form either type of team, how many are in the fraternity? The fraternity had 13 members and could field 3,003 teams of either type The fraternity had 15 members and could field 3,003 teams of either type The fraternity had 17 members and could field 3,003 teams of either type The fraternity had 21 members and could field 3,003 teams of either type

Yes 0.5455 approximately, the gambler is on the safe side. If the probability that a team will win any particular game is p, the chance of winning the Series is p4 + 4p4 (1 - p) + 10p4 (1-p)2+20p4 (1-p)3. If this expression is equal to .4, p will be equal to .4539 approximately. Hence B's chance of winning the first game is .5461. Since odds of 6 to 5 cor- respond to a probability of only .5455 approximately, the gambler is on the safe side.

An expert gives team A only a 40% chance to win the World Series. Basing his calculation on this a gambler offers 6 to 5 odds on team B to win the first game. Is his judgment sound? Yes No Maybe Cannot be determined

251/256 sunk = 251/256 escape = 5/256

Assume that a single depth charge has a probability of 1/2 of sinking a submarine, 1/4 of damage and 1/4 of missing. Assume also that two damaging explosions sink the sub. What is the probability that 4 depth charges will sink the sub?

Valid If the conclusion were not valid, then every tree'would have a different number of leaves; and you'd run out oI leaves before you ran out of trees. It's valid.

Assume that every tree has at least one leaf. If there are more trees than there are leaves on any one tree, then there exist at least two trees with the same number of leaves. Is the conclusion valid? Valid Invalid Cannot say

Align the hour hand with the sun's azimuth, and south will be midway between the hour hand and 12.

Assuming the sun rises at 6:00 a.m., sets at 6:00 p.m., and moves at a uniform rate, how can a lost boy scout determine south by means of a watch on a cloudless day? Align the hour hand with the sun's azimuth, and north will be midway between the hour hand and 12. Align the hour hand with the sun's azimuth, and south will be midway between the hour hand and 12. Align the hour hand with the sun's azimuth, and south will be midway between the hour hand and 6. Align the hour hand with the sun's azimuth, and north will be midway between the hour hand and 16.

25 mile The distance from Kroflite to Beeline must be at least 25 miles- The towns could then be located at distances 0,1.,4, 1'0,-18,23, and 25 miles from Kroflite. There are 21 distances between towns and these are all distinct. Any shorter distance would mean at least one duplication.

Between Kroflite and Beeline are five other towns. The seven towns are an integral number of miles from each other along a straight road. The towns are so spaced that if one knows the number of miles a person has traveled between any two towns he can determine the particular towns uniquely. What is the minimum distance between Kroflite and Beeline to make this possible ?* 15 miles 25 miles 30 miles 35 miles

The misspelling of errors and receive are, of course, the first two errors. The third error is simply that there are only two errors in all.

DI LALABAS There are three errers in the statement of this problem. You must detect all of them to recieve full credit.

2,1,3 2, 1, and 3. The sequence represents the number of chimes of a wall clock which strikes once on the half hour.

Determine the next three terms of the sequence 12, 1, 1, 1, ... 12,1,1 2,1,3 2,1,1 4,5,6

Numbers (door, gates, etc) Dr. LaRouche was buying numbers (for doors, gates, etc.) and the price was ten cents per digits

Dr. Furbisher LaRouche, the noted mathematician' was shop- ping at a hardware store and asked the price of certain articles' The salesman replied, "One would cost 10 cents' eight would cost 10 cents, seventeen would cost 20 cents' one hundred and four would cost 30 cents, seven hundred and fifty six would also cost 30 cents, and one thousand and seventy two would cost 40 cents. What was Dr' LaRouche buying?* Numbers (door, gates, etc) Medicine Produce Cannot be determined

PYX (a religious vessel)'

ERRONEOUS IF LUMABAS A safe has three dials shown above. It will open only when a three-letter word is indicated by the dials even in permuted form. What is that word? PYX (a religious vessel)'

1001! + 2 ...... 1001! + 1001.

Find 1000 consecutive nonprime numbers.

A is lying If we assume B is telling the truth, then by following the im- plication of his statement we find that D is also telling the truth. If we assume B is lying, we find -that C and E are telling the truth. In either event, however, A is lying. Thus A is the only suspect we know with certainty to be lying.

Five suspects were rounded up in connection with the famous "Cock Robin Murder" Their statements were as follows: A:"C and D are lying" B: "A and E are lying" C: "B and D are lying" D: "C and E are lying" E: "A and B are lying" Who is lying? A is lying B is lying C is lying D is lying

Gwen loves Alan

Four boys, Alan, Brian, Charles and Donald, and four girls, Eve, Fay, Gwen and Helen are each in love with one of the others, and, sad to say, in no case is their love requited. Alan loves the girl who loves the man who loves Eve. Fay is loved by the man who is loved by the girl loved by Brian. Charles loves the girl who loves Donald. If Brian is not loved by Gwen, and the boy who is loved by Helen does not love Gwen, who loves Alan? Gwen loves Alan Helen loves Alan Fay loves Alan Eve loves Alan

4 hearts A - 4 B - 3 C - 2 Insofar as Dave is concerned the points taken in by the winners could be distributed among them in any manner without affect- ing has $42 loss. Assume one player got them all. Then (D-O) +(D-0)+D-(26-D)=42, and D=17, so Dave took 4 hearts and the queen of spades. By similar reasoning, Arch, Bob, and Chuck took in 4, 3, and 2 hearts, respectively.

Four players played a hand of hearts at $1 a point (pairwise payoffs). Dave lost $10 to Arch, $12 to Bob, and $20 to Chuck. How many hearts did poor Dave take in? 2 3 4 5

600

Hard Knox College is a member of a six-school basketball league in which every pair of schools plays each other twice. The other five schools ended the season with respective league records of.200, .300, .500, .600, and .800. How did Hard Knox make out? 300 500 600 800

8 It can be done with eight colors, one for each row, since a bishop move always involves a change of row. That no smaller number will do is seen from the fact that the main diagonals can have no color repeats.

How many colors are necessary for the squares of a chessboard in order to assure that a bishop cannot move from one square to another of the same color? 5 6 7 8

136

How many three digit telephone area codes are possible given that: (a) the first digit must not be zero or one; (b) the second digit must be zero or one; (c) the third digit must not be zero; (d) the third digit may be one only if the second digit is zero.

White 6 ; Black = 4

If 2 marbles are removed at random from a bag containing black and white marbles, the chance that they are both white is 1/3. If 3 are removed at random, the chance that they all are white is 1/6. How many marbles are there of each color? White 8 ; Black = 2 White 2 ; Black = 4 White 6 ; Black = 4 White 6 ; Black = 2

432516

If all 720 permutations of the digits 1 through 6 are arranged in numerical order, what is the 417th term?

100% drink liquor.

In Bristol 90% of the citizens drink tea; 80% drink coffee; 70% drink whiskey; and 60% drink gin. No one drinks all four beverages. What percent of Bristol's citizens drink liquor?

2nd player wins If the 1st player marks one square, the 2nd marks two to form a connected right angle. If instead he marks 2 or 3 squares, the 2nd player marks as many as necessary to complete either an L or a T of 5 squares. In either event, the 2nd player wins.

In Greenwich Village, tic-tac-toe is played in an unusual way. At each turn a player marks as many squares as he wishes pro- vided they are in the same vertical or horizontal row (they need not be adjacent). The winner is the one who marks the last square. Which player has the advantage and what strategy should he employ? 1st player wins. 2nd player wins None wins Winner cannot be determined

zero Consequently, the probability of making 16 the hard way is zero.

In Puevigi, the game of craps is played with a referee calling the point by adding together the six faces (three on each die) visible from his vantage point. What is the probability of making 16 the hard way? (That is, by throwing two eights.) 0 1/2 1/3 2/3

average loss of a quarter a game In the long run, the three black balls will occur equally spaced in the stream of balls which emerge. The player, therefore, can expect three white balls to appear before the first black ball and hence will show an average loss of a quarter a game.

In a carnival game, 12 white balls and 3 black balls are put in an opaque bottle, shaken up, and drawn out one at a time. The player gets 25 cents for each white ball which emerges before the first black ball. If he pays one dollar to play, how much can be he expect to win (or lose) on each game? verage loss of a quarter a game verage loss of a nickel a game verage loss of a dime a game verage loss of a penny a game

25. In order to avoid pitching the last half of the ninth inning, Hi had to be on the losing side. Thus he must have allowed at least one run, which would have required at least one pitch. 24 more pitches were necessary to produce 24 outs.

In a fast Major League baseball game, pitcher Hi N. Outside managed to get by with the minimum number of pitches possible. He played the entire game, which was not called prior to completion. How many pitches did he make? 10 25 30 35

30 straight walks Mudville got 30 straight walks. Casey, batting ninth, was picked off first base while bowing to the southside bleachers after his initial walk, and was picked off third the next time while doffing his cap to the fans on the northside. While bowing to the umpire after the 30th walk forced him home, he neglected to touch home plate and was declared out in the dugout.

In a memorable game with the Podunk Polecats, the Mudville Mets established a record. They received the maximum number of walks possible in one inning in which one player (who happened to be the Mighty Casey) was up three times and accounted for all three outs. How many walks did Podunk allow in that tedious half-inning? 30 straight walks 40 straight walks. 20 straight walks 10 straight walks.

8,677,690 This is readily evaluated to be 8,677,690, the number of posi- tive integers all of whose digits are distinct.

In the binary system there are only two positive integers con- taining no digit more than once, namely 1 and 10. How many are there in base ten? 8,677,690 8,777,690 8,667,690 8,666,690

11/16 (about 69%)

In the final seconds of the game, your favorite N.B.A. team is behind 117 to 118. Your center attempts a shot and is fouled for the 2nd time in the last 2 minutes as the buzzer sounds. Three to make two in the penalty situation. Optimistic? Note: the center is only a 50% free-thrower. What are your team's overall chances of winning? 11/16 5/27 1/2 6/43

NO Not at all. Every closed boundary must contain at least one pair of perpendicular segments forming an L. The 2nd player, therefore,.can avoid defeat by completing each of his opponent's potential L's, drawing the foot whenever. the 1st player makes a vertical connection and the upright whenever he makes a horizontal one.

In the game of "connecto", 2 players alternate in joining adjacent points, horizontally or vertically, on an infinite rectangular lattice, one using solid lines for his connections, the other, dashes. The winner is the first to enclose a region of any shape by a boundary composed of his symbol only. (The player with the dashes has won above). Is the 2nd player doomed to defeat? YES NO MAYBE CANNOT BE DETERMINED

Yes. The first player should appropriate the only unique point by placing the first cigar vertically on its flat end over the center of the table. From then on he can counter each of his opponent's moves by "reflecting" them through the center of the table.

In the game of "stogey' two players alternately place cigars on a rectangular table with the restriction that each new cigar must not touch any of the previously placed cigars. Can the 1 st player assure himself of victory if we define the loser as the first player who finds himself without sufficient room to place a cigar? Yes No Maybe Cannot be determined

Let 1, 2, 3, and 4 denote the amount of the bids in increasing order and consider the 24 possible permutations. The home- owner will optimize his chances by looking at the first bid and using it as a standard, i.e., by accepting the first subsequent bid, if any, which is less or the last if none is smaller. His chance of accepting the lowest bid is easily seen to be 11/24. If he uses the lower of the first two bids as his standard instead, then his chance is reduced to 10/24.

MALABO LUMABAS Four swimming pool builders submit sealed bids to a homeowner who is required by law to accept the last bid that he sees, i.e., once he looks at a bid, he automatically rejects all previous bids. He is not required to open all the envelopes, of course. Assuming that all four bids are different, what procedure will maximize his chances of accepting the lowest bid. and what will be the probability of doing so?

It's love, violets, vile sot, I've lost.

MALABO LUMABAS "12'3 4567," I thought. "I'll woo my lady fair With 6154723." Alas, at greater cost My rival (6147 352!) staked out his claim With orchids dear to maidens' hearts. 1'67 4532! There are four anagrams to decipher in this cryptogram. 35467 12! It's love, violets, vile sot, I've lost.

"What is so rare as a daY in June?"

MALABO LUMABAS "ABCD EF FG HCHI CF C JCK EL MNLI?" an appren- tice poetician asked Archimedes O'Toole. (Question enciphered by simple substitution.) "How about February 29th for openers?" retorted Arch. What was the apprentice's question? "What is so rare as a daY in June?"

"There are 3 ways to pronounce 'slough'."

MALABO LUMABAS The student above can't decide whether to write "to," "too," or "two". In point of fact, the sentence can be spoken but not written. Can you give an example of a sentence that can be written but not spoken "There are 3 ways to pronounce 'slough'."

136,852,887,600 and 66,905,856,160, more than two to one in favor of the 4-4-3-2 distribution.

MALABONG LUMABAS What is the most likely distribution of the suits in a hand at Bridge? (It is not 4-3-3-3.)

1.5

Martian coins are 3-sided (heads, tails, and torsos), each side coming up with equal probability. Three Martians decided to go odd-man-out to determine who pays a dinner check. (If two coins come up the same and one different, the owner of the latter coin foots the bill). What is the expected number of throws needed in order to determine a loser? 1.5 2.5 3.5 4.5

Colonel Downing

Mary Ann Moore's father has a yacht and so has each of his four friends: Colonel Downing, Mr. Hall, Sir Barnacle Hood, and Dr. Parker. Each of the five also has one daughter and each has named his yacht after a daughter of one of the others. Sir Barnacle's yacht is the Gabrielle, Mr. Moore owns the Lorna; Mr. Hall the Rosalind. The Melissa, owned by Colonel Downing, is named after Sir Barnacle's daughter. Gabrielle's father owns the yacht which is named after Dr. Parker's daughter. Who is Lorna's father? Colonel Downing Mr. Hall Sir Barnacle Hood Dr. Parker

Yellowstone = 0.486 ; Bermuda 0.514 Max = 105/216 = 0.486 Bermuda, with a probability of 0.514 is the betting favorite.

Max and his wife Min each toss a pair of dice to determine where they will spend their vacation. If either of Min's dice displays the same number of spots as either of Max's, she wins and they go to Bermuda. Otherwise, they go to Yellowstone. What is the chance they'll see "Old Faithful" (Yellowstone) this year? Yellowstone = 0.486 ; Bermuda 0.514 Yellowstone = 0.514 ; Bermuda 0.486 Yellowstone = 0.492 ; Bermuda 0.534 Yellowstone = 0.534 ; Bermuda 0.492

9 p.m. or 3 a.m.

Maynard's Grandfather Clock is driven by two weights, one for the striking mechanism which strikes the hours only' the other for the time mechanism. When he hears the clock strike his bedtime' he immediately winds the clock and retires. After winding, the weights are exactly opposite each other. The weights are again opposite every six hours thereafter. What is Maynard's bedtime? 9 p.m 3. a.m both 9 p.m. or 3 a.m. none of the above

One Liberal Art Student; First Student There is only one liberal arts student. If the third is in liberal arts, then he;s lying and the first really is not in liberal arts. But the word ..really,' implies he said he was a liberal arts student, which is impossible. Hence the third cannot be in liberal arts, and thus the first is"

On a certain campus liberal arts students always lie and engineers always tell the truth. A stranger meets 3 students and asks the first if he is studying liberal arts. The first answers the question, but the stranger doesn't hear him. The second student then says that the first denied being a liberal arts student. Then the third student says that the first is really a liberal arts student. How many are liberal arts students? Can we decide which? One Liberal Art Student; First Student One Liberal Art Student; Second Student One Liberal Art Student; Third Student Two Liberal Art Student; First and Third Students

4! or 24

On a certain day, our parking lot contains 999 cars, no two of which have the same 3 digit license number. After 5:00 p.m. what is the probability that the license numbers of the first 4 cars to leave the parking lot are in increasing order of magnitude ? 12 24 72 128

1/750 21/125 - 1/6

One of a pair of dice is loaded so that the chance of a 1 turning up is 1/5, the other faces being equally likely. Its mate is loaded so that the chance of a 6 turning up is 1/5, the other faces being equally likely. How much does this loading increase the probability of throwing a 7 with the two dice? 1/750 1/850 1/900 1/950

3 a group of three is possible. If A marries B's sister, B marries C's sister, and C marries A's sister, a group of three is possible. An additional mutual brother-in-law, however, is not possible without violating either the laws of bigamy or consanguinity.

Rigorously speaking, two men are "brothers-in-law" if one is married to the full sister of the other. How many men can there be with each man a brother-in-law of every other man? 2 3 4 5

No; he has already used 4 minutes, the time that he has to go the whole 2 miles.

Rufus T. Flypaper drives two miles to work every morning- Very precise, he knows he must average 30 mph to arrive on time. One morning a woman driver impedes him for the first mile, cutting his average to only l5 mph. He quickly calculated his proper speed for the rest of his trip to arrive on time. Assume that his car could do 120 mph. Could he arrive on time? Yes No Maybe Can not be determined

10 Any counting interval from 1 through 9 will result in another team member's selection. Joe will be captain if he chooses 1.0.

Six boys on a hockey team pick a captain by forming a circle and counting out until only one remains' Joe is given the option of deciding ihat number to count by. If he is second in the original counting o-rder what number should he choose? 6 8 10 12

3.7 dollars. If the total weight amounts to 60 ounces, then the grocer from whom I did not Purchase a packet gives short weight. If the total weight is 593/a ounces, then the Srocer from whom ,I purchased one packet gives shorl weight, etc-

Six grocers in a town each sell a different brand of tea in four ounce packets at 25 cents per packet. One of the grocers gives short weight, each packet of his brand weighing only 37.75 ounces. If I can use a balance for only one weighing, what is the minimum amount I must spend to be sure of finding the grocer who gives short weight?' 3.7 dollars. 4.7 dollars. 5.2 dollars. 6.3 dollars.

0.1 His chance of being shot is that or about .067. Hence his survival probability is enhanced about 0.1 by spinning.

Six men decide to play Russian roulette with a six gun loaded with one cartridge. They draw for position, and afterwards, the sixth man casually suggests that instead of letting the chamber rotate in sequence, each man spin the chamber before shooting. How would this improve his chances? 0.1 0.2 0.6 0.12

2/3

Smith and Jones, both 50% marksmen, decide to fight a duel in which they exchange alternate shots until one is hit. What are the odds in favor of the man who shoots first?* 1/3 2/3 1/2 2/5

0, 3, 6, 8 Without safeties, only one answer is possible: 0, 3, 6, 8. The 3rd period score could come either from a touchdown or 2 field goals. The 4th period score had to come from a touch- down plus a 2-point conversion.

State University won their first football game of the season 17 to 0. Though they scored no safeties, they managed to score more points each quarter than they had scored in the previous quarter. What were State's quarter scores? 0, 2, 6, 8 0, 3, 6, 8 0, 3, 8, 10 0, 2, 6, 10

300 miles.

Stations A and B are 120 miles apart on a single-track railroad' At the same time that a train leaves A for B at 25 mph, a train leaves B for A at l5 mph. Just as the first train leaves A, a South American botfly flies from the front of the engine straight toward the other train at IOO mph. On meeting the second train it immediately turns back and flies straight for the first train. It continues to fly back and forth with undiminished speed until it is crushed in the eventual collision. How far had the fly flown ? 120 100 200 300

Chicago is the proper site Assume the site is not Chicago. Pair each non-Chicagoan with a Chicagoan. Moving the site to Chicago will not inJrease the total mileage. In fact, since there are unpaired Chicagoans, it will decrease it. Hence Chicago is the proper site, regardless of the geographic distribution of the other members.

The League Against Restrictive Diets, with members all over the U.S., plans a convention. Most of the members live in Chicago, so they feel that city is the logical site. The other members suggest some city representing the "weighted centroid" of the League. If the object is to minimize total distance traveled by the members of the L.A.R.D., who is right? Chicago is the proper site Chicago is not the proper site Cannot be determined

(x.y) is a member only if y is the nearest state capital to state capital x.

The following pairs are members of a certain relation: (Sacra- mento, Carson City), (Pierre, Bismark), (Juneau, Olympia), and (Albany, Hartford). Moreover, the reversals of the first two pairs are also members, while those of the latter two are not. What is the relation? (x.y) is a member only if y is the nearest state capital to state capital x.

yes Very easily. He takes the center square and then counters each of his opponent's moves by taking the diametrically opposite square.

The game of reverse tic-tac-toe (known to some as toe-tac-tic) has the same rules as the standard game with one exception" The first player with three markers in a row loses. Can the player with the first move avoid being beaten? * yes no maybe cannot be determined

3/5

The local weather forecaster says "no rain" and his record is 2/3 accuracy of prediction. But the Federal Meteorological Service predicts rain and their record is 3/4. With no other data availa- ble, what is the chance of rain?

15 AND 16 THIRD GROUP ; 17 IN SECOND The first group consists of numbers written only with curves (in a certain type style), the second group consists of numbers written only with straight lines and the third group consists of numbers written with both straight lines and curves. Therefore 15 and 16 would be in the third group and 17 in the second.

The numbers are divided into three groups as follows: 0,3,6,8,9, ... in the first group, 1,4,7,11,14, ... in the second group and 2,5,10,12,13, ... in the third. In which groups would 15,16 and 17 be placed? * 15 AND 16 THIRD GROUP ; 17 IN SECOND 15 AND 16 SECOND GROUP ; 17 IN THIRD 15 AND 17 THIRD GROUP ; 16 IN SECOND 15 AND 17 SECOND GROUP ; 16 IN THIRD

Included among the 18 children were 8 married couples.

The passengers on an excursion bus consisted of 14 married couples, 8 of whom brought no children, and 6 of whom brought 3 children apiece. Counting the driver, the bus had 31 occupants. How is this possible? Included among the 18 children were 6 married couples. Included among the 18 children were 8 married couples. Included among the 18 children were 5 married couples. Included among the 18 children were 7 married couples.

No. Removing opposite corners leaves 32 squares of one color and 30 squares of another color. However, each domino covers one square of each color.

Two squares are removed from opposite corners of a checker- board leaving 62 squares. Can the checkerboard be filled with 31 dominoes, each domino covering two adjacent squares? Yes No Maybe Cannot be determined

20 in Set A, 21 in Set B 20 is in A, 21 is in B. Set A contains numbers with an even (B with an odd) number of letters in their literal representation.

The set A contains the integers 0,4,5,9,11,12,13,14,19, .... The set B contains 1,2,3,6,7,8,10,15,16,17,18, .... Place 20 and 21 in their proper sets. 20 in Set A, 21 in Set B 21 in Set A, 20 in Set B Both in Set A Both in Set B

500

There are four volumes of an encyclopedia on a shelf, each volume containing 300 pages, (that is, numbered 1 to 600), but these have been placed on the shelf in random order. A book- worm starts at the first page of Vol. 1 and eats his way through to the last page of Vol. 4. What is the expected number of pages (excluding covers) he has eaten through?

C choose 4

There are n points on a circle. A straight line segment is drawn between each pair of points. How many intersections are there within the circle if no 3 lines are collinear?

80

There are three families, each with two sons and two daughters' In how many ways can all these young people be married?

No. For example, Tom could have shot 3, 4, and 5 followed by 15 4's, Dick 4, 5, and 3 followed by 15 4's and Harry 5, 3, 4, followed by 15 4's, in which case Tom would end 1 up on Dick, Dick 1 up on Harry, and Harry 1 up on Tom.

Tom, Dick, and Harry played a round of golf, each ending with a total of 72 strokes. Each pair competed against each other in match play (most holes won). Tom beat Dick, and Dick beat Harry. Does it follow that Tom beat Harry? Yes No Maybe Cannot be determined

2/21

Three dart players threw simultaneously at a tic-tac-toe board, each hitting a different square. What is the probability that the three hits constituted a win at tic-tac-toe?

1

Three marksmen simultaneously shoot at and hit a rapidly spinning spherical target. What is the probability that the three points of impact are on the same hemisphere? 1/3 1/2 1 1/5

Yes Yes, by considering the throws in pairs and deleting each occurrence of HH or TT. Since HT and TH are equiprobable, one may be used to denote 0, the other, 1.

Using a "true" coin, a random sequence of binary digits can be generated by letting, say heads denote zero and tails, one. An operations analyst wished to obtain such a sequence, but he had only one coin which he suspected was not true. Could he still do it? Yes No Maybe Cannot be determined

yes Among many solutions we offer one: number the square in horizontal rows as follows and start the ,,Knights Tour" with the square numbered 1, proceeding in serial order: 1., 40, !3, 26,3, 50, 15,28;24, 37,2,39, 14,27,4, 49;41, 12, ZS,5g, 51, 62,'29, 1.6; 36,23,38, 6L, 54, 57, 4g,5;1,!, 42, 59, 56, 63, 52-, 77, 30; 22, 35, 64, 53, 60, 55, 6, 47;

Using graph paper to simulate a board of 64 squares and starting anywhere, is it possible to move a Knight to all squares without touching the same square twice? Move can be made from A to either B. yes no maybe cannot be determined

four specimens With four specimens, the odds in favor of a mated triple are only 4/9. *But if payload limitations permit five to travel to Earth, the odds go up to 50/81.*

Venusian batfish come in three sexes, which are indistinguishable (except by Venusian batfish). How many live specimens must our astronauts bring home in order for the odds to favor the presence of a "mated triple" with its promise of more little batfish to come? 1 2 3 4

198 days. Every day it increased its height by one half of its original height. In 198 days, it reproduced its height 99 times and was therefore 100 times its original height.

Very few people are aware of the growth pattern of Jack's bean-stalk. On the first day it increased its height by 1/2, on the second day by 1/3, on the third day by 1/4, and so on. How long did it take to achieve its maximum height (100 times its original height)? 198 200 201 202

2 Two. The 4th and the 11th

What is the least number of links that must be disengaged from a 23-link chain so that any number of links from 1 to 23 can be obtained by taking one or more of the pieces? 1 2 3 4

319 or 316

What is the longest legal sequence of bids in a single contract bridge hand? 255 319 567 892

N if we consider the letters as the fIrst letters in one, two, three, four, fIve, six, seven, eight, nine.

What letter follows OTTFFSSE? N O T E

each class is empty

What property is common to Arctic penguins, peacock eggs, the Hungarian Merchant Marine, the University of Chicago football team, 19 point cribbage hands and the solution set of the equation e^e^x = 1? each class is empty

The two events are equally improbable. The maximum point count involves 4 aces, 4 kings, 4 queens and a jack. Since the jack can be in any suit, there are also 4 ways of achieving this 37 point hand. Thus the two events are equally improbable.

Which is the more unlikely event in bridge: the ultimate in distribution (a 13 card suit) or the ultimate in point count? he ultimate in distribution the ultimate in point count the two events are equally improbable the two events are equally probable

79 By noticing the progression of the second digits, you might have deduced that this is the sequence of reversals of 2-digit primes in ascending order. The last member is 79.

With some sharp reasoning, you ought to be able to determine the last member of the sequence for which the first 20 mem- bers are: 11, 31, 71, 91, 32, 92, 13, 73, 14, 34, 74, 35, 95, 16, 76, 17, 37, 97, 38, 98, ? 79 52 32 10

$9.99

You and a friend spot a loose $20 bill simultaneously and agree to an auction in which you write down your bids and compare them. High bidder gets the $20 and pays the other the amount of the higher bid. Tie bidders split the $20. How much do you bid?