Gotcha Puzzles

Ten trick puzzles to keep you on your toes.

Posted Sep 24, 2019

In an ingenious 1982 collection of puzzles, called Gotcha, the late brilliant puzzle-maker Martin Gardner used the word “gotcha” to identify a genre that involves any puzzle that aims to dupe the solver through some form of trickery.

Gotcha puzzles fall generally into two categories: (1) puzzles that surreptitiously use specific words deceptively, or (2) puzzles that cleverly structure the puzzle statement in a way that is designed to lead the solver astray. Here is an example: 

How much dirt is there in a hole that is 1 foot wide by 1 foot long by 1 foot deep? By the way, the hole is in the middle of a rectangular container.

If your answer was 1 cubic foot of dirt, you fell into the puzzle’s trap. Obviously, there is no dirt in a hole inside a container. A hole has nothing in it, by definition. 

The ten gotcha puzzles provided here are classic ones. You may have seen them in other contexts, but even so, they always seem to produce the same kind of annoyance that results from being duped, no matter how many times we have come across them. There is something intrinsic about such puzzles that intrigues us. Perhaps they may, in their own way, illustrate how easily we can be deceived. Whatever the truth of the matter, gotcha puzzles will keep you on your toes.

Puzzles

1. In my hand, I have two current U. S. coins. The two add up to 15¢. One of the two coins is not a nickel. So, what possible coins could they be?

2. My wonderful cousin, who owns a large farm, showed me something he did the other day: he put three and seven-ninths haystacks in one part of his field, and two and two-thirds haystacks in another part. He then put the haystacks together. How many haystacks did that produce?

3. In a peaceful town just outside Utah, the residents love to watch trains passing through on two tracks that run parallel, except for a place under a tunnel where they merge into a single track. Yesterday, a train entered the tunnel going in one direction and another entered the tunnel going in the opposite direction. Both trains were moving at top speed, yet there was no collision. Why?

4. Is it legal in California for a man to marry his widow’s sister? 

5. A bull is put on a weighing scale. He is so huge that only three of his four legs fit on the scale. The scale shows 1,000 pounds. How much do you estimate the bull weighs when he stands on all four legs?

6. It takes twelve 1-dollar stamps to make a dozen. So, how many 2-dollar stamps does it take to make a dozen?

7. After a series of arduous experiments, a famous chemist discovered that it took eighty minutes for a specific chemical reaction to occur when she was wearing her eyeglasses, but that it took the same reaction an hour and twenty minutes to occur when she was not wearing them. Why?

8. What two whole numbers, not fractions, make 13 when they are multiplied together?

9. Do you think that the product of the first ten digits is between 100 and 1,000, or is greater than 1,000?

10. I bought a new expensive pot the other day. If it takes three minutes to boil an egg in the pot, how long would it take to boil three eggs?

Answers

1. The puzzle says that there are two coins that add up to 15¢, and that one of the two coins is not the 5¢ coin; so, the only conclusion is that the other coin is the nickel. More specifically, one of the two coins is a dime (a 10¢ coin), while the other one is the nickel.

2. One huge haystack. If you do not see the “gotcha” in this puzzle, replace haystacks with feathers. Let’s say that in one part of your living room, you make three and seven-ninths piles of feathers (approximately, of course). In another room, you make two and two-thirds piles of feathers (again, approximately). Now put the piles together. How many piles of feathers do you now have? One pile of feathers.

3. The trains entered the tunnel at different times.

4. The situation is impossible. The “gotcha” in this puzzle is the word widow. A man who leaves a widow is a dead man, of course! So, how can a dead man marry his widow’s sister?

5. The bull weighs 1,000 pounds, no matter if it stands on four legs or on three. Standing on a weighing scale will show someone's weight, whether or not the person lifts one foot up. 

6. Giving the price of a stamp is the source of the "gotcha" trick in this puzzle. To make a dozen stamps, you will need twelve stamps, period. These can be 1-dollar each (that is, twelve stamps costing 1-dollar each will make a dozen); these can be 2-dollars each (that is, twelve stamps costing 2-dollars each will also make a dozen); these can be 3-dollars each (that is, twelve stamps costing 3-dollars each will likewise make a dozen); and so on. The puzzle asks how many stamps (not their values) there are in a dozen. The answer is, of course, twelve.

7. Since one hour is equal to 60 minutes, then one hour and twenty minutes is, of course, equal to 60 + 20 = 80 minutes. So, there is nothing to explain, because it took the reaction 1 hour and 20 minutes, or in equivalent terms, 80 minutes to occur, no matter what the chemist was wearing.

8. The only two whole numbers that make 13 when multiplied together are 13 itself and 1. As you might know, this is true of any prime number, such as 13.

9. The product of the first ten digits is zero, because the set of the first ten digits—0, 1, 2, 3, 4, 5, 6, 7, 8, 9—includes 0 among them. Any number or sequence of numbers multiplied by 0 will equal 0.

10. You would not normally boil three eggs separately, one after the other with the pot. If you did, you would, of course, need three minutes to boil the first egg, then another three minutes to boil the second egg, and then again another three minutes to boil the third egg—or nine minutes in total. But, if you boil one, two, three, or any number of eggs at one time in the pot, then it will take only three minutes.