Enigma 1417: Magic circle
29 June 2013
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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?