Button Cycles - A Proposed New Problem

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CSFPython     2025-01-24 08:45:18

This is intended to be a problem where there is no immediate sense of a method of solution. I hope that there is nothing readily available on-line as this would spoil the problem. My intention is that you have to spend some time investigating the behaviour of the problem before you begin to get ideas for a possible solution. It is not an easy problem but it has the potential to be very rewarding.

Rodion (admin)     2025-01-24 13:52:38
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Dear Clive, thanks for the problem!

About the data-setting code taking few seconds - as recently there was a small improvement which made input data loading so to say "asynchronously" after the problem page is already shown - now the data-generation could work even up to 30 seconds (the limit on response waiting somewhere in the web-server).

gardengnome     2025-01-25 07:22:57
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Are there any particular constraints on n, x and y? For example, is the following case included?

53 0 1
OXOXOXOXOXOXOXOXOXOXOXOXOXOXOXOXOXOXOXOXOXOXOXOXOXOXO
CSFPython     2025-01-25 09:53:16

Mathias,

The value of N is chosen randomly in the range 5 to 100. The values of x and y are also chosen randomly, provided that they are different and that each is less than N. The starting pattern is chosen randomly provided that it does form part of a cycle. Provided that your example starting position is part of a cycle then the example could be chosen.

The Setter rejects some random choices on the grounds that they would be too easy to solve. The example given in the problem description would be rejected on this basis. The Setter also rejects any random choice where the answer would be greater than 2^63 or where the solution time would be too long. I hope this is helpful.

gardengnome     2025-01-28 20:32:33
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That. Was. Hard.

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