## December 2016

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All the solutions we present are built on splitting the N persons into groups and running the rope-pulling contest in subsets of these groups.

Here's an N=27 solution:

- ABCDEFGHI WXY Z ; JKLMNOPQ RSTUV

- ABCDEFGHI Z 0 ; JKLMNOPQ WXY

- ABCDEFGHI ; RSTUV WXY Z

- JKLMNOPQ Z ; RSTUV WXY 0

An N=30 solution:

- ABCD EFGHI JKLMNO ; PQRSTUV WXYZ0123

- ABCD PQRSTUV ; EFGHI JKLMNO

- JKLMNO PQRSTUV ; EFGHI WXYZ0123

- ABCD WXYZ0123 ; EFGHI PQRSTUV

To verify that the last solution works, you need to show that the integer solutions for the following equation set

( 1 1 1 -1 -1 ) (x4) (0) ( 1 -1 -1 1 0 ) (x5) (0) ( 0 -1 1 1 -1 ) (x6) = (0) ( 1 -1 0 -1 1 ) (x7) (0) (x8)are multiple of (4,5,6,7,8), which means that all the participants are from the same gender as required.

An N=114 solution for five rope-pulling contests can be achieved by

1 -1 -1 1 -1 1 -1 1 0 1 -1 0 1 1 0 -1 -1 1 1 0 1 1 -1 -1 1 1 -1 0 1 -1

with the only integer solution as follows:

9 12 20 22 25 26