The Rearrangement Puzzle

November 4, 2015

On the topic of puzzles, my puzzle in in the NYTimes Numberplay column this week. It’s built to look hard, but come apart easily if you attack it from the right direction.

The Rearrangement Puzzle

The number 1, 525, 354, 555, 657, 585, 950 is, as it happens, evenly divisible by 99.
Fix all the 5s digits where they are in the number, and rearrange the other digits randomly.
What is the chance that a rearrangement of this form is still evenly divisible by 99?

I have mixed feelings about this puzzle. On the one hand, I love that it looks so hard, but can be unraveled so easily once you get past that, and attack it with the right tools (hints at Numberplay). On the other hand, I’m dissatisfied with its inability to generalize to other puzzles, or begin a larger investigation.

Perhaps it does, and I’ve just lost the scent.

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