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 Indecisive Walk (Posted on 2023-08-17)
Marilyn vos Savant still has her column in Parade magazine, which introduced everyone to the Monty Hall Problem. Here's her latest (well, a repeat from 1995):

A schoolboy has a test coming up and so wants to study for it, but is conflicted, as there's a movie he wants to see playing at the local theater. He starts out toward the theater, but halfway there he has second thoughts and turns back toward home. But again, halfway home he has third thoughts and turns back again, this time toward the theater, but again, halfway there he turns back toward home, and this indecision continues in the same way with the same switching ad infinitum.

What does this lead to as to his location in the long run?

 Submitted by Charlie No Rating Solution: (Hide) Marilyn claims that the boy's asymptotic behavior is to "quiver like a tuning fork" 1/3 of the way from his home to the theater. This is a false analogy from Zeno's paradox. She claims that "the sum of his forward motion totals 2/3 of the way from his house, but the backward motion totals 1/3 of that distance and is subtracted from the 2/3. But that is only considering the positions at even numbers of steps. After an odd number, the boy is 2/3 of the way to the theater. Actually he's not "quivering like a tuning fork". but repeatedly going back and forth the full 1/3 of the home-to-theater distance, between 1/3 of the way and 2/3 of the way.: A listing of his location after each step. Each line shows the location after walking toward the theater, and each location after the second part of that pair. Position 0 is his home; position 1 is the theater: ```clearvars,clc pos=0; for i=1:30 newPos=(pos+1)/2; pos=newPos/2; fprintf('%10d %17.15f %17.15f\\n',[i newPos pos]) end pair position of after going after going walks toward movie toward home 1 0.500000000000000 0.250000000000000 2 0.625000000000000 0.312500000000000 3 0.656250000000000 0.328125000000000 4 0.664062500000000 0.332031250000000 5 0.666015625000000 0.333007812500000 6 0.666503906250000 0.333251953125000 7 0.666625976562500 0.333312988281250 8 0.666656494140625 0.333328247070312 9 0.666664123535156 0.333332061767578 10 0.666666030883789 0.333333015441895 11 0.666666507720947 0.333333253860474 12 0.666666626930237 0.333333313465118 13 0.666666656732559 0.333333328366280 14 0.666666664183140 0.333333332091570 15 0.666666666045785 0.333333333022892 16 0.666666666511446 0.333333333255723 17 0.666666666627862 0.333333333313931 18 0.666666666656965 0.333333333328483 19 0.666666666664241 0.333333333332121 20 0.666666666666060 0.333333333333030 21 0.666666666666515 0.333333333333258 22 0.666666666666629 0.333333333333314 23 0.666666666666657 0.333333333333329 24 0.666666666666664 0.333333333333332 25 0.666666666666666 0.333333333333333 26 0.666666666666667 0.333333333333333 27 0.666666666666667 0.333333333333333 28 0.666666666666667 0.333333333333333 29 0.666666666666667 0.333333333333333 30 0.666666666666667 0.333333333333333 ```

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 Subject Author Date Solution Larry 2023-08-17 09:03:41 Solution Jer 2023-08-17 08:35:58
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