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 Magic circle (Posted on 2006-12-16)
Joe placed 10 numbered counters in a circle:

```
0

1                   2

8                               7

4                               5

6                   3

9

```

He asked Penny to pick a number and then count clockwise from that numbered position on the circle that many further counters. For example, if she picked 7, the new counter would be 1 (located 7 clockwise from the 7). Repeating the process with the number on each new counter she would finish up at zero.

There was one particular number that, if she started there, she would go through all the other counters before getting to zero. What was that number?

Penny also found that, if she rearranged the counters in the circle in a certain order, leaving the topmost three (1, 0 and 2) in place (and maybe some others), that if she started with that same numbered counter from part 1, that she would also go through all the other counters before getting to zero. What was the clockwise order of the numbers in this new arrangement, starting with the zero at the top?

 See The Solution Submitted by Charlie No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: Solution | Comment 4 of 6 |
(In reply to Solution by Penny)

If you start with the clockwise sequences shown in the first column below, the sequence of visited markers are on the right.

Note that the first two rows have only 9 of the 10 markers visited, the 3 remaining unvisited.  Subsequent lines have more missed counters:

`0246738591   9  5  4  8  7  2  6  1  00246835791   9  7  8  4  5  2  6  1  00256478931   9  8  4  3  2  6  1  00256738941   9  8  7  2  6  1  00264578931   9  8  5  1  0`
` `

I think you were starting from the same position (5), rather than the same numbered counter (9).

Edited on December 19, 2006, 8:54 am
 Posted by Charlie on 2006-12-19 08:50:26

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