The Unofficial IEEE Brainbuster Gamebook: Mental Workouts for the Technically Inclined / Edition 1

by Donald R. Mack

Overview

"...Made my head hurt! — Isaac Newton...Doesn't bug me! — Grace Hopper...Rang my chimes! — Alexander Graham BellThese innovative, witty, and utterly outrageous brainbusters engage reasoning power while honing problem-solving skills. Beginning with easier puzzles, then getting progressively harder, this tantalizing collection will increase brain power with each puzzle conquered. Also included is a special Solutions section that gives a detailed answer to each brainbuster."

Product Details

ISBN-13:	9780780304239
Publisher:	Wiley
Publication date:	08/14/1992
Pages:	144
Product dimensions:	5.00(w) x 8.07(h) x 0.38(d)

About the Author

Donald R. Mack is the author of The Unofficial IEEE Brainbuster Gamebook: Mental Workouts for the Technically Inclined, published by Wiley.

Read an Excerpt

The Unofficial IEEE Brainbuster Gamebook

Mental Workouts for the Technically Inclined

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By Donald R. Mack

John Wiley & Sons

ISBN: 0-7803-0423-3

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Chapter One

Problems Requiring Only Logic

1.1. Lined up ill the dusty stacks of a college library are the volumes of IEEE Potentials. Each volume consists of four issues, each 5 mm thick. The front and back covers of each volume are 4 mm thick. A bookworm begins at the first page of volume 1, issue I and eats in a straight line until she reaches the last page of volume 3, issue 4. How far does the bookworm eat? 1.2. If you have a five-liter and a three-liter bottle and plenty of water, how can you get four liters of water in the five-liter bottle?

1.3. You encounter three people who know each other. One always tells the truth, one lies all the time, and one gives random answers. How can you tell, by asking only three questions directed to only one person at a time, which is which?

1.4. You have 10 sets of 10 coins each. Each of the coins weighs 10 grams, except for the coins in one set, which weigh 9 grams each. All 100 coins look alike. How can you identify the set of 9-gram coins with only one weight measurement?

1.5. In Bill's sock drawer are eight pairs of white socks and six pairs of red socks. (He's a snappy dresser.) How many socks does Bill have to pick at random to be sure he has a matched pair? 1.6. This problem is for chess players. Place a knight in one of the corner squares of a chessboard. Using his move, land in all 64 squares without reaching the same square twice.

1.7. Connect the nine points below with four straight lines, without lifting the pencil from the paper.

1.8. This one is easy, too, if you don't make an unstated assumption. Make four equilateral triangles with these six sticks of equal length:

1.9. Three engineers rented a hotel room that was supposed to cost $40 for the night (a long time ago). The desk clerk mistakenly charged them $15 each, payable in advance. Later he realized he had overcharged them, but couldn't figure out how to divide the five-dollar refund among the three engineers. So he pocketed two dollars and returned one dollar to each of the engineers. The engineers ended up paying $14 each, or $42. That, plus the clerk's two dollars, added up to $44. What happened to the other dollar?

1.10. At a political convention there are 100 politicians. Each one is either crooked or honest. At least one is honest. Given any two of the politicians, at least one is crooked. How many are honest and how many are crooked?

1.11. The inhabitants of North Strangeland are of either type A or type B. Type A people can ask only questions whose correct answer is "yes." Those of type B can ask only questions whose correct answer is "no," George was overheard to ask, "Are Nancy and I both type B?" Which type is Nancy?

1.12. In South Strangeland, sane humans and insane vampires make only true statements. Insane humans and sane vampires make only false statements. Two sisters, Anna and Betsy, live there. We know that one is a human and one is a vampire, but we know nothing about the sanity of either. Anna says, "We are both insane." Betsy replies, "That's not true!" Which sister is the vampire?

1.13. I have two coins that total 55 cents. One of them is not a nickel. What are the two coins?

1.14. An archeologist walking along the shore of the Mediterranean Sea finds an old Roman coin. On one side is the face of Julius Caesar and the date 44 BC. On the other side is an olive tree. The archeologist says, "This coin is counterfeit." How does she know?

1.15. There are nine coins in a bag. One of them is counterfeit. A real coin weighs one gram and a counterfeit one weighs 0.9 gm. You have a balance. How can you identify the counterfeit coin with two weighings?

1.16. Two friends, George and Harry, were born in May, one in 1964 and the other a year later. Each has an antique 12-hour clock. One clock loses 10 seconds an hour and the other gains 10 seconds an hour. On a day in January the two friends set both clocks right at exactly 12 noon. "Do your realize," says George, "that the clocks will drift apart and won't be together again until ... good grief, your 23rd birthday!" How long will it take for the two clocks to come together again? Which friend is the older, George or Harry?

1.17. The dean of engineering had three 4.0 seniors, one of whom was blind. To decide which one would be the valedictorian, he devised a tie breaker. He explained to the students that he had collected five hats: three white and two red. Then when their eyes were closed he put one on each student's head. "Now open your eyes," he said, "and tell me the color of the hat on your head." After a while one of the students who could see said, "I can't be sure." A minute later the second said, "Neither can I." Then "Alia!" cried the blind student. "My hat must be white!" Please explain how the blind student accomplished this impressive reasoning.

1.18. In a remote village in Asia everyone either tells the truth all the time or lies all the time. An English-speaking traveler encounters two of the villagers and asks Mr. A, "Are you a truth teller or a liar?" Unfortunately Mr. A speaks no English, so Mr. B translates the question and the answer, and replies to the traveler, "Mr. A says he is a liar." Now, which is Mr. B, a truth teller or a liar?

1.19. Two trains, each moving at 50 km/hr, were approaching each other on the same track. When they were 100 km apart, a bee on the front of one train started flying toward the other train at a steady ground speed of 60 km/hr. When it reached the other train, it immediately started back toward the first train. It continued to fly back and forth until the trains collided. How far did it fly? Incidentally, the bee escaped.

1.20. An oarsman leaves his boathouse on the river and rows upstream at a steady rate. After 2 km he passes a log floating down the river. He continues on for another hour, and then turns around and rows back downstream. He over takes the log just as he reaches the boathouse. What is the flow velocity of the river?

1.21. I know two lumberjacks. The little lumberjack is the son of the big lumberjack, but the big lumberjack is not the little lumberjack's father. Who is the big lumberjack?

1.22. A monk started up a hill one morning and reached the top at sunset. He stayed overnight in the temple there, started back down the hill the next morning by the same path, and arrived at the bottom at sunset. Was there a place on the path that he passed at exactly the same time of day going both ways?

1.23. This one is difficult. A married couple invited other married couples to a party. Including the host and hostess, there were ncouples. As people arrived, they shook hands with only the people they had not met before. Eack person already knew his or her own partner, of course. After everyone had arrived, the host asked each person, including the hostess, how many times he or she had shaken hands. To everyone's surprise, each person responded with a number different from everyone else's. How many times did the hostess shake hands? For extra credit, calculate how many time the host shook hands.

1.24. Draw the next figure without lifting the pencil off the paper or retracing any line.

1.25. The people who live on the east side of the city of Loopbow always tell the truth, and the people who live on the west side always lie. During the day the people mingle on both sides. What one question can you ask a resident picked at random to determine which side of the city you are in?

1.26. A traveler is driving to Millinocket. He comes to a fork in the road and sees a farmer. The farmer is from one of two families, one who are truth tellers, and one who always lie. What question can the traveler, knowing this, ask the farmer to find out which is the road to Millinocket? 1.27. Please find the words whose initials are on the right side of each equation below. The first answer is shown.

1. 26 = L of the A (Letters of the alphabet) 2. 7 = W of the AW 3. 1,001 = AN 4. 12 = S of the Z 5. 54 = C in a D (including the J) 6. 9 = P in the SS 7. 88 = K on a P 8. 13 = S on the AF 9. 32 = DF at which WF 10. 18 = H on a G C 11. 90 = D in a RA 12. 200 = D for P G in M 13. 8 = S on a SS 14. 3 = BM(SHTR) 15. 4 = Q in a G 16. 24 = H in a D 17. 1 = W on a U 18. 57 = HV 19. 11 = P on a FT 20. 1,000 = W that a P is W 21. 29 = Din Fin a LY 22. 64 = S on a C 23. 40 = D and N of the GF

1.28. How can you distribute 1023 coins in 10 bags so that you can provide any number of coins without opening a bag? Start with the low numbers. You need a bag with just one coin in it, and one with just two, but you don't need a bag with just three, etc. 1.29. A strange monetary system has been proposed that will use International Monetary Units, or IMUs, instead of dollars or yen. All prices will be in integral numbers of IMUs. The money will consist of paper bills in 10 denominations that will allow you to make any purchase from 1 to 1023 IMUs without having to use more than one bill of each denomination. What should the denominations of the bills be? For extra credit, explain why showing the value of each bill and the prices of purchases in binary numbers would simplify paying for a purchase.

1.30. Please fill in the blank. Pedro is the son of Juan. Juan is the of Pedro's father.

1.31. An engineer got a flat tire. After removing the four lug nuts from the wheel, he accidentally dropped all four down a sewer drain. He knew that the wheel would stay on with only three lug nuts. He thought of stealing three nuts from one of the cars parked nearby, but that would be dishonest, and the stolen nuts probably wouldn't fit anyway. Can you suggest a practical solution to his problem?

1.32. You have six bottles of pills. All of the pills look alike and each weighs one gram, except for the pills in one of the bottles that weigh two grains each. How can you determine, with one weighing, which bottle contains the two-gram pills? You don't need a balance. A spring scale will do.

1.33. On one side of a river are the king (K), the queen (Q), the prince (P), the princess (PR), a guard (G), and the guard's wife (W). They have to cross the river in a two-passenger rowboat, so only one or two can cross at a time. They are all able to row the boat. The crossings are subject to two ridiculous conditions:

None of the royal family may travel with a commoner.

No man may be on the same side of the river with a woman other than his wife, even if he is in the boat and she is on the shore, or vice-versa, unless the woman's husband is present.

What is the sequence of trips that will get all six people across the river?

1.34. What are the next two letters of this sequence?

O T T F F S S __

1.35. Sketch the next two symbols in this sequence:

1.36. A gold miner lives at point A, six km north of the river on the map below. His mine is at point B, 15 km from his cabin and three km north of the river. He cant go directly to work because his burro has to stop at the river on the way, for a drink. At what point on the river should he water the burro, to minimize the length of the trip?

1.37. I have a chain of 23 paper clips. If I remove two of them, I can make a chain of any length from one to 23 out of the five pieces. Which two should I remove?

1.38. A fastidious fellow wears a clean shirt every day. Every Friday morning he drops off the week's laundry and picks up the previous week's laundry. How many shirts must he have?

1.39. A student purchased his books for the spring quarter. He noticed that all but two had blue covers, all but two had red covers, and all but two had green covers. How many books did he have?

1.40. On the shelf are three cans, labeled "NUTS," "BOLTS," and "NUTS AND BOLTS." We know that the labels are mixed, so that none is on the right can. How many samples must we take (without looking into the cans) to establish the correct labeling?

1.41. What is the largest amount of change in U.S. coins you can have in your pocket and still not have change for a dollar bill?

1.42. There are four students of different weights, heights, and ages. The freshman, who is the youngest, is shorter than the sophomore, who is the heaviest. The sophomore is younger than the junior, who is the tallest. How does the senior compare with the others if no one occupies the same rank in any two of the categories?

1.43. A creative teacher arranged the chairs for her students in five rows, with four chairs per row. But there were only 10 students. How did she arrange the chairs?

1.44. How can you cut a round pizza into eight pieces with three cuts? Don't try any tricks like retracing a cut, folding the pizza, or removing it from the pan.

1.45. Next are four views of the same cube. Which face is opposite the C?

1.46. The square below has an area of 64 square units. When its parts have been reassembled to form the rectangle, the area is 65 square units. What's wrong?

1.47. Eight cardboard squares of equal size are stacked as shown on the next page. Please number them, starting with the one on the bottom.

See if you can decode the following puzzles. Here is an example:

MAN Solution: Man overboard BOARD

1.48. ALL world

1.49. SYMPHON

1.50. GROUND FEET FEET FEET FEET FEET

1.51. J YOU U ME S T

1.52. STAND I

1.53. WEAR LONG

1.54. CYCLE CYCLE CYCLE

1.55. DICE DICE 1.56. EILN PU

1.57. NaCl.[H.sub.2]O NaCl.[H.sub.2]O CCCCCCC

1.58. WHEATHER

1.59. LE VEL

1.60. 1 3 5 7 9 WHELMING

1.61. [(CAPITALISM).sup.HE]

1.62. B L O U S E

1.63. STANDING FRIENDS FRIENDS

1.64. ECNALG

1.65. O B.S. M.S. Ph.D. 1.66. ZERO DEGREE DEGREE DEGREE

1.67. ONCE LIGHTLY

1.68. NOON GOOD 1.69. STROKES strokes strokes

1.70. AGE BEAUTY

1.71. MAN campus

1.72. GETTINGITALL

1.73. D DEER E R

1.74. R | E | A | D | | I N | G

1.75. T O U C H

1.76. HOU SE

1.77. John's father has three children. One is Richard, who lives in Chicago. Another is Margaret, who lives in Vancouver. Who is the third? 1.78. Susie ChemE, conducting an experiment in the chemistry laboratory, poured 54 cc of water into a beaker from a graduated cylinder. Then she accidentally dropped the cylinder and broke it. She had meant to pour only 50 cc of water into the beaker. She found three large identical test tubes, and with eight pourings back and forth between the test tubes and the beaker she was able to end up with 50 cc in the beaker. Can you duplicate her feat? Susie had a steady hand and could pour equal amounts of water into two or three test tubes. Consider such an operation as one pouring.

(Continues...)

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Table of Contents

Preface.

Problems Requiring Only Logic.

Problems Requiring Some Mathematics.

Little Engineering Problems.

Solutions to the Problems.

Acknowledgments.