Games for the Superintelligent

Practically all of us tend to take it for granted that intelligence is a good thing and lack of intelligence a bad thing. A little reflection will show that it's not so simple. Being bright can create real problems, and very bright people often suffer under handicaps undreamed of by their less gifted brethren. Nor are these, as one might suppose, simply the burdens imposed by a heightened awareness, a greater sense of life's complexities, a more poetic and sensitively tuned soul. They are, on the contrary, distressing in quite practical ways and they almost always start early. The following conversation between a second-grade teacher and a bright pupil is a case in point:

Teacher: I'm going to read you a series of numbers: one, two, three, four, five, six, seven. Now, which of those numbers can be divided evenly by two?

Pupil: All of them.

Teacher: Try again. And this time, think.

Pupil (after a pause): All of them.

Teacher: All right, how do you divide five evenly by two?

Pupil: Two and a half and two and a half.

Teacher: If you're going to be smart-alecky, you can leave the room.

The story is, I am sorry to say, a true one. So is another story, of a high school student, told by educator Alexander Calandra: Asked on an examination to describe a method for finding the height of a building by using a barometer, the student, bright enough to be bored by the obvious answer, decided to (continued on page 120)Superintelligent(continued from page 105) describe not one but two alternate methods: Take the barometer, he wrote, and drop it from the top of the building, timing the interval until you see it smash on the ground. Then, using the standard formula for acceleration of a falling object, calculate the height of the building. Or, he went on, find the owner of the building and say to him, "If you'll tell me how tall your building is, I'll give you a good barometer." At last report, the student was in trouble both with his teacher and with his school's hierarchy.

Intelligence, of course, is a problem not just to the young. A study at the University of Michigan revealed that executives with high I. Q.s are as likely to create problems as to solve them--to stumble over their own brains, as one report expressed it. Businessmen with only average I. Q.s, being less apt to confuse themselves with a multiplicity of factors, are often much better problem solvers. On the other hand, it must be admitted that being bright does have some undeniable pleasures, and it's one especially beguiling subspecies of those pleasures that this article is all about. But how can you tell whether or not these mental push-ups and deep knee bends are for you? And how serious a symptom is it if they aren't?

First, it's a good idea to remember that intelligence isn't any single, readily definable quality but a complicated assortment of many different qualities. Some of us possess some of them, some of us possess others. Intelligence tests have been campaigned against on precisely those grounds--that too many of them treat intelligence as if it were a single identifiable thing, like red hair or double-jointed thumbs. The fact is that no one knows exactly what intelligence is. The only thing of which we're absolutely certain is that intelligence tests measure what intelligence tests measure. Yet we all agree, somehow, that there is such a thing as intelligence. We are all likely to agree, too, that it is parceled out quite unequally among the human species.

It's been shown that I. Q.--which is nothing more than intelligence in relation to an individual's chronological age--has certain characteristics. Researchers have discovered, for example, that it normally stops increasing at the beginning of adolescence (except in the case of certain very bright people whose intelligence may continue developing until 18 or so). This is not to say that the ability to use one's brain power cannot be improved well beyond that time. In fact, a reader who can work his way through the following puzzles will probably discover a number of mental techniques that had not previously been in his armamentarium. He will be, it is true, fundamentally no brighter than when he started, but he may be able to do more with his intelligence. For that reason, he may actually score slightly higher on an I. Q. test. And he will certainly look more intelligent to anyone watching him unerringly solve an unfamiliar problem.

The typical puzzle, especially the kind most admired by the superintelligent, has its roots in mathematics, in one or another variety of logic or in words, or it may be based on a combination of these. We offer here puzzles that are a maddening mélange of those three elements. Most of them have a kind of do-it-with-mirrors difficulty. That's precisely what makes them the charming diversions they are. They require some logical (or, on occasion, illogical) leap that, in human terms, is the rough equivalent of a monkey in a cage suddenly realizing that it can use a stick to reach a banana: no stick, no banana. And so it is here: no leap, no solution. If that seems obscure now, it won't take you long to see what we mean.

1. A snail is at the bottom of a well 30 feet deep. It can crawl upward three feet in one day, but at night it slips back two feet. How long does it take the snail to crawl out of the well?

2. How many nines are there from one to 100?

3. Punctuate the following so it makes sense: John while James had had had had had had had had had had had a better effect on the teacher.

4. Three boxes are labeled Apples, Oranges and Apples and Oranges. Each box is labeled incorrectly. You may select only one fruit from one box. (No feeling around or peeking permitted.) How can you label each box correctly?

5. All readers of this article greatly love puzzles. Some readers of this article are famous. Some famous people are great lovers. Therefore:

a. All readers of this article are famous.

b. All great lovers are puzzling.

c. Some famous people love puzzles.

d. Some readers of this article are great lovers.

6. Move two matches and make four squares:

7. What eight-letter word contains only one vowel?

8. What word contains all five vowels in alphabetical order?

9. What word contains three sets of double letters in a row?

10. There are two jars of equal capacity. In the first jar there is one amoeba. In the second jar there are two amoebas. An amoeba can reproduce itself in three minutes. It takes the two amoebas in the second jar three hours to fill the jar to capacity. How long does it take the one amoeba in the first jar to fill that jar to capacity?

11. Draw four connected straight lines, without retracing your path, that pass through all the points:

12. Three intelligent men, applying for a job, seem equal in all pertinent attributes, so the prospective employer, also an intelligent man, sets a simple problem for them. The job, he says, will go to the first applicant to solve it. A mark is placed on each man's forehead. The three are told that each has either a black mark or a white mark, and each is to raise his hand if he sees a black mark on the forehead of either of the two others. The first one to tell what color he has and how he arrived at his answer will get the job. Each man raised his hand, and after a few seconds one man came up with the answer. What color was his mark and how did he figure it out?

13. Man: How many birds and how many beasts do you have in your zoo?

Zookeeper: There are 30 heads and 100 feet.

Man: I can't tell from that.

Zookeeper: Oh, yes you can.

Can you?

14. A hunter arose early, ate breakfast and headed south. Half a mile from camp, he tripped and skinned his nose. He picked himself up, cursing, and continued south. Half a mile farther along, he spotted a bear. Drawing a bead, he pulled the trigger, but the safety was on. The bear saw him and headed east at top speed. Half a mile farther, the hunter caught up, fired, but only wounded the beast, which limped on toward the east. The hunter followed and half a (continued on page 210)Superintelligent(continued from page 120) mile farther, caught and killed it. Pleased, the hunter walked the mile north back to his camp to find it had been ransacked by a second bear.

What color was the bear that tore up his camp?

15. One bucket contains a gallon of water, another a gallon of alcohol. A cup of alcohol from the second bucket is poured into the bucket of water. A cup of the resulting mixture is then poured back into the bucket of alcohol. Is there: (a) more water in the alcohol than alcohol in the water? (b) more alcohol in the water then water in the alcohol? (c) the same amount of water in the alcohol as alcohol in the water?

16. What do the following words have in common? deft, first, calmness, canopy, laughing, stupid, crabcake, hijack.

17. Some Playboy readers are geniuses. All geniuses have some human virtues as redeeming qualities. Therefore:

a. Playboy readers all have some virtue.

b. All geniuses are quality Playboy readers.

c. Some Playboy readers have redeeming qualities.

18. C, G, Q are to F, V, R as T, X, H are to: (a) V, L, G; (b) B, F, Y; (c) W, M, I; (d) N, Z, D.

19. This is an engineering drawing, two views of an object:

What is the side view like? What is the perspective view?

20. A ship is at anchor. Over its side hangs a rope ladder with rungs a foot apart. The tide rises at the rate of eight inches per hour. At the end of six hours, how much of the rope ladder will remain above water, assuming that eight feet were above water when the tide began to rise?

21. A camp cook wants to measure four ounces of vinegar out of a jug, but he has only a five-ounce and a three-ounce container. How can he do it?

22. Andy dislikes the catcher. Ed's sister is engaged to the second baseman. The center fielder is taller than the right fielder. Harry and the third baseman live in the same building. Paul and Allen each won $20 from the pitcher at pinochle. Ed and the outfielders play poker during their free time. The pitcher's wife is the third baseman's sister. All the battery and infield, except Allen, Harry and Andy, are shorter than Sam. Paul, Andy and the shortstop lost $50 each at the race track. Paul, Harry, Bill and the catcher took a trouncing from the second baseman at pool. Sam is involved in a divorce suit. The catcher and the third baseman each have two children. Ed, Paul, Jerry, the right fielder and the center fielder are bachelors. The others are married. The shortstop, the third baseman and Bill each cleaned up $100 betting on the fight. One of the outfielders is either Mike or Andy. Jerry is taller than Bill. Mike is shorter than Bill. Each of them is heavier than the third baseman.

Using these facts, determine the names of the men playing the various positions on the baseball team.

Answers

1. Twenty-eight days. On the 28th day, the snail reaches the top of the well. Once there, it does not, of course, slip backward.

2. Twenty. Did you forget 90, 91, etc?

3. John, while James had had "had," had had "had had." "Had had" had had a better effect on the teacher.

4. Pick a fruit from the Apples and Oranges box. If it turns out to be an orange, since all the boxes are wrongly labeled, the box label must be changed to Oranges. The remaining boxes contain apples and apples and oranges, but which contains which? Simple. Remember that the boxes are all mislabeled. Simply switch the two remaining labels.

5. C.

6.

7. Strength.

8. Facetious.

9. Bookkeeper.

10. Three hours and three minutes. Once the amoeba in the first jar has reproduced itself (a process that takes three minutes), that jar is at the same point at which the second jar started.

The only difference is that it is three minutes behind.

11.

12. Since all three applicants raised their hands, there were two possibilities: two black and a white or three black marks. If there were a white mark on any forehead, two men would see one black and one white and would instantly deduce that the third mark must be black. Since this instant solution did not occur, each of the three men saw two black marks. Therefore, all were black, including the mark of the successful applicant.

13. There are 10 birds and 20 animals. The problem may be expressed in equation form as follows, letting A represent animals and B represent birds:

A + B = 30

4A + 2B = 100

14. White. It is a polar bear, for the North Pole is the only place where you can go one mile south, one mile east and one mile north and still end up at your starting point.

15. C.

16. All of them contain three consecutive letters of the alphabet in alphabetical order.

17. C.

18. C.

19.

20. Since the ship is afloat, the water level in relation to the ship stays the same. Therefore, eight feet are above the water at the end, just as at the beginning.

21. Pour the five-ounce container full from the jug. Pour the three-ounce container full from the five-ounce container, leaving two ounces remaining in the five-ounce container. Pour the three-ounce container back into the jug. Then pour the two ounces remaining in the five-ounce container into the three-ounce container. Pour the five-ounce container full from the jug. Fill the remaining one ounce of the three-ounce container from the five-ounce container and four ounces are left in the five-ounce container.

22. Harry is the pitcher, Allen the catcher, Paul the first baseman, Jerry the second baseman, Andy the third baseman, Ed the shortstop, Sam the left fielder, Mike the right fielder and Bill the center fielder.