## Problem of the Day #294: Cowmpanions and EnemoosJanuary 7, 2012

Posted by Saketh in : potd , trackback

Farmer John gave Bessie and the girls friendship bracelets for Cowmas. The bracelets came with a huge supply of beads in $10$ different cowlors. Each bracelet can have either $0$ or $1$ bead of each cowlor.

Within the herd, any two cows are either cowmpanions or enemoos. The cows want to decorate their bracelets such that, looking only at the beads assigned to a given pair of cows, it is immediately possible to determine whether or not they are cowmpanions.

At most how many members can the herd have for this tagging system to work? Please help Farmer John solve this tricky cowmbinatorics problem.