MathDB

Largest possible size of subset S of T

Source: Baltic Way 2011

November 6, 2011

combinatorics proposedcombinatorics

Problem Statement

Let

T

denote the

15

-element set

\{10a+b:a,b\in\mathbb{Z},1\le a<b\le 6\}

. Let

S

be a subset of

T

in which all six digits

1,2,\ldots ,6

appear and in which no three elements together use all these six digits. Determine the largest possible size of

S