Tangled Tale

shoelace puzzle

A shoelace is lying on the floor, and I’m too nearsighted to see how the lace crosses itself at points A, B, and C. If I pull on the ends, what’s the probability that it will produce a knot?

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distance sums problem

What location on this line segment has the smallest sum of distances to the labeled points?

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Club Med

My doctor wants to establish a dosage for a new drug, so he gives me a bottle of 48 pills and tells me to take them throughout the month of June. I can take as many or as few as I like on any given day, so long as I take at least 1 pill each day. Show that there’s a sequence of consecutive days during which I take exactly 11 pills.

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Assume that these statements are true:

  1. Not all Futility Closet readers are U.S. residents.
  2. All walrus veterinarians who are not U.S. residents are not Futility Closet readers.
  3. Do 1 and 2 imply that

  4. Not all Futility Closet readers are walrus veterinarians?
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Ones in a Million

Of the integers from 1 to 1,000,000, which are more numerous: the numbers that contain a 1 or those that don’t?

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The Figure 8 Puzzle

figure 8 puzzle

Can this loop of string be freed from its wire? Stewart Coffin, who devised the puzzle in 1974, writes, “I soon became convinced that this was impossible, but being a novice in the field of topology, I was at a loss for any sort of formal proof.” He published the challenge in a newsletter and has been receiving requests for a solution ever since. Adding to the confusion, in 1976 a British puzzle editor mistakenly claimed with that Coffin’s creation was equivalent to another puzzle with a known solution, and Pieter van Delft and Jack Botermans published an amusingly bewildering “solution” of their own in their 1978 book Creative Puzzles of the World.

In the meantime, fans around the world have continued to experiment, and mathematicians Inta Bertuccioni and Paul Melvin have both offered proofs that the puzzle is unsolvable. “Whoever would have guessed that this little bent piece of scrap wire and loop of string would launch itself on an odyssey that would carry it around the world?” Coffin writes. “Will it mischievously rise again, perhaps disguised in another form, as topological puzzles so often do?”