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Maximal size of a set of naturals with 5 conditions

Source: Baltic Way 2006

December 4, 2010
combinatorics proposedcombinatorics

Problem Statement

Determine the maximal size of a set of positive integers with the following properties:
1.1. The integers consist of digits from the set {1,2,3,4,5,6}\{ 1,2,3,4,5,6\}.
2.2. No digit occurs more than once in the same integer.
3.3. The digits in each integer are in increasing order.
4.4. Any two integers have at least one digit in common (possibly at different positions).
5.5. There is no digit which appears in all the integers.
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