December 2016
<<November December January>>
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