Lesson Planning: Use It or Lose It: Puzzles to Exercise the Brain

1. Mystery Number Solution The mystery number is 3476. Start with 5, 3, and 1 for the thousands digit. Eliminate 5, since you can't double it to get the ones digit. Now you have 3 and 1 and the possibilities are 3**6 or 1**2. Since the ones digit is one less than the tens digit, you can have 3*76 or 1*32. Finally, the hundreds digit is the difference between the tens digit and the thousands digit, so the two possibilities are 3476 or 1232. But, since no two digits can be the same, the number must be 3476.
2. Brainbinders Puzzle 2002 Solution Fold the bottom third of the rectangle up at the line and the top third down at the line to form a rectangle with one blue side and one gold side. Click here to see a visual representation of the puzzle solution.
3. Brain Teaser Puzzle 84 Solution. The camel can take 500 bananas to its family. Technically, the camel can take 533.333 extra bananas. However, the preferred answer is that the camel should travel 250 miles, leave 1,000 bananas there and go back and get more. The camel should go back and forth until all the bananas are at the 250 mark. Then the camel should take all the bananas to the 500-mile mark, then the 750 mark, then to the end. That way, the camel will end up with 500 bananas at the finish.
4. Book Solution The woman will never finish the book.
5. Prisoner's Dilemma Solution There is no single best strategy. The successful strategy depends on the strategy adopted by one's opponent, and is often one that increases the payoff to both players. Serendip uses a particular strategy, called "tit for tat," which is believed to be optimal under the widest possible set of partner strategies.
6. Geometry Puzzle: Bear Solution There are two possible solutions: (1) The hunter's door is a foot or so from the North Pole, facing north, so that his position in front of the door is precisely upon the North Pole. Since that's a ridiculous place to build a house and since bears do not roam within 50 miles of the Pole, the bear is either imaginary or imported, and there is no telling what color it is. (2) The hunter can go 50 miles south, 50 miles west, and 50 miles north and end up where he started. Consider the parallel of latitude close enough to the South Pole that its length is 50/n miles, for some integer n. Take any point on that parallel of latitude and pick the point 50 miles north of it. Situate the hunter's front porch there. The hunter goes 50 miles south from his porch and is at a point we'll call A. He travels 50 miles west, circling the South Pole n times, and is at A again, where he shoots the bear. Fifty miles north from A, he is back home. Since bears are not indigenous to the Antarctic, again the bear is either imaginary or imported and there is no telling what color it might be.
7. Logic Puzzle 29 Solution Each person paid \$9, totaling \$27. The manager has \$25 and the bellboy \$2. The bellboy's \$2 should be added to the manager's \$25 or subtracted from the tenants' \$27, not added to the tenants' \$27.
8. Riddle 8 Solution The word is few.
9. The Fork in the Road Solution If we assume that the logician's question requires a yes or no answer, there is more than one solution: The logician points to one of the roads and says to the native, "If I were to ask you if this road leads to the village, would you say yes?" If the road does lead to the village, the liar would say no to the direct question, but as the question is put, he lies and says he would respond yes. Thus the logician can be certain that the road does lead to the village, whether the respondent is a truth-teller or a liar. On the other hand, if the road actually does not go to the village, the liar is forced in the same way to reply no to the inquirer's question. The logician says, "Of the two statements, 'You are a liar' and 'This road leads to the village,' is one and only one of them true?" Here again, a yes answer indicates it is the road, a no answer that it isn't, regardless of whether the native lies or tells the truth.
10. The Counterfeit Coins Solution The counterfeit stack can be identified by a single weighing of coins. Take one coin from the first stack, two from the second, three from the third and so on to the entire ten coins of the tenth stack. Then weigh the whole sample collection on the pointer scale. The excess weight of this collection, in number of grams, corresponds to the number of the counterfeit stack. For example, if the group of coins weighs 7 grams more than it should, then the counterfeit stack must be the seventh one, from which you took seven coins (each weighing 1 gram more than a genuine half-dollar). Even if there had been an 11th stack of ten coins, the procedure just described would still work; no excess weight would indicate that the one remaining stack was counterfeit.