Problem

Source: IX International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

Tags: table, combinatorics



A square is divided into 169 identical small squares and in every small square is written 0 or 1. It isn’t allowed in one row or column to have the following arrangements of adjacent digits in this order: 101, 111 or 1001. What is the the biggest possible number of 1’s in the table?