**From New Scientist #2577, 11th November 2006**

Joe placed 10 numbered counters in a circle (as shown) and asked Penny to pick a number. Then he asked her to count clockwise that number of counters to find a new counter. For example, if she picked 7 the new counter would be 1. Repeating the process with the number shown on each new counter she would finish up at zero.

But if she picked one particular number first she would reach zero via all the other counters. Penny found that leaving some of the counters in place, including 0, 1 and 2, there was another arrangement of the counters that had this same property if she started at the same number.

Beginning with zero, what was the clockwise order of Penny’s numbers?

[enigma1417]

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*Related*

This puzzle is similar to Enigma 1421.

This Python 3 program (it uses the

yield fromconstruct) runs in 173ms. It would probably be more efficient to check the potential sequences forward starting from the start number we’ve determined, but we’ve already written the`solve()`

routine, so we use that and check if any solution starts from the number we want.Solution:Penny’s numbers are: 0, 2, 6, 4, 7, 9, 3, 5, 8, 1.