A heap of a positive integer number of matches (that is, no broken matches) are divided into five groups.

If we take as many matches from the first group as there are in the second group and add them to the second, and then take as many from the second group as there are in the third group and add them to the third, and, so on ...... until finally, we take as many from the fifth group as there are in the first group and add them to the first group - the number of matches in each of the groups would be equal to the same positive integer.

What is the minimum number of matches in each group at the beginning?

If the initial sizes of the groups are a, b, c, d and e, then, after the first four transfers, just before the final transfer, the numbers would be:

a-b, 2b-c, 2c-d, 2d-e, 2e

Then, after the final transfer:

2(a-b), 2b-c, 2c-d, 2d-e, 2e-a+b

However, I can't get from the set of equations where each of these values are equal, anything other than all the variables equal to zero.

Posted by Charlie on 2012-02-26 13:19:46