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Three puzzles from Martin Gardner (1914-2010)

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News of Martin Gardner’s death began circulating on Saturday night. For those of you who are unfamiliar with his work, here’s a taste of the kinds of puzzles he was famous for bringing to the world. Of course, he did much more: 15 years ago, I had the great honor of meeting him and his wife for a profile of him, which you can read here.

I still have the trick pen he gave me as a souvenir, one that I’ll show anyone who comes by my desk. (I’ll try to post a video of the pen.) It brings back fond memories of being shown his stash of magic tricks and gag gifts, his thoughtful comments on irrational beliefs, his experiences with mathematicians like Paul Erdős and the Gardners’ feeding of feral kittens that came to the back deck of the house every afternoon.

Rest in peace, Martin.

1. Reversed Trousers
Each end of a 10-foot length of rope is tied securely to a man’s ankles. Without cutting or untying the rope, is it possible to remove his trousers, turn them inside out on the rope and put them back on correctly? Party guests should try to answer this confusing topological question before initiating any empirical tests.
2. Crazy Cut
This one looks much easier than it is. You are to make one cut (or draw one
line)—of course, it needn’t be straight— that will divide the figure into two identical parts.





3. Out with the Onion
Arrange four paper matches on a table as shown at right. They represent a martini glass. A match head goes inside to indicate the onion of a Gibson cocktail. The puzzle is to move just two matches so that the glass is re-formed, but the onion—which must stay where it is—winds up outside the glass. At the finish, the glass may be turned to the left or the right, or even be upside down, but it must be exactly the same shape as before.





The figures below are not a solution, because the onion is still inside or because three matches have been moved.











 1. To reverse a man’s trousers while his ankles are joined by a rope, first slide the trousers off onto the rope, then push one leg through the other. The outside leg is reversed twice in the process, leaving the trousers on the rope right-side out but with the legs exchanged and pointing toward the man’s feet. Reach into the trousers from the waist and turn both legs inside out. The trousers are now reversed on the rope and in position to be slipped back on the man, zipper in front as originally arranged but with the legs interchanged.
2. The figure is cut into congruent halves like this:






3. Arrange the matchsticks like this:

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  1. 1. grymoire 1:27 pm 05/23/2010

    All hail the puzzle master! (With apologies to Will Shortz. I’m sure he’ll understand.)

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  2. 2. RangerSasquatch 2:26 pm 05/23/2010

    In the problem called Crazy Cut you say the resulting two pieces will be "identical" but in the result you state that the halves are "congruent." These terms do not mean the same thing as the usage of "identical" in the problem implies outline as opposed to "congruent’s" implication of equal area. Makes it hard to solve if the setup is thusly flawed. Not fair.

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  3. 3. itai 2:47 pm 05/23/2010

    @ RangerSasquatch: have another look: the two pieces are identical, in the sense that you mean: rotate the right piece 90 degrees clockwise.
    BTW "congruent" indeed means "has identical shape", in geometry.

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  4. 4. RolandSlinger 11:34 pm 05/23/2010

    @RangerSasquatch – You seem to misunderstand the meaning of the word "congruent." For two shapes to be congruent, they have to have exactly the same outline, which seems to mean the same thing as "identical" to me.

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  5. 5. Johnay 12:00 pm 05/25/2010

    I got them all, though my solution to the pants problem was a bit different in that I turned them inside-out and vise-versa as they were taken off and put on.

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  6. 6. andybaird 5:10 pm 05/30/2010

    "Reversed Trousers" is unsolvable as stated. Note the starting condition: "Each end of a 10-foot length of rope is tied securely to a mans ankles." The use of "ankles"–plural–implies that each end is tied to BOTH ankles, making it impossible to remove the trousers. For the given solution to work, the initial condition would have to be "Each end of a 10-foot length of rope is tied securely to ONE OF a mans ankles."

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  7. 7. podisco 10:11 pm 06/5/2010

    The bottom of the martini glass is slid halfway to the right making it the bottom of the new upside down martini glass. The old stem remains as a side of the upside down martini glass and the former left side of the glass is moved down to become the right side of the new upside down martini glass with the onion on the outside. The new glass is not the same dimensions as the old glass, but is the same shape.

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  8. 8. ivanoschen 9:07 pm 06/10/2010

    The solution to "Crazy Cut" is problematic. Note the condition of "one line". One line shall not produce any angle, as produced in the solution provided above.

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  9. 9. BeckyJL 1:56 am 10/22/2014

    The FAR simpler solution to the pants problem is simply to peel the pants off, starting from the waist, turning them inside out as you go. As the ankles of the pants are finally peeled off the feet, the pants are ALREADY inside out, on the rope. I couldn’t figure out what the brain teaser was, as this is how I remove sweat pants, even without ropes tied to my ankles!

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