The numbers 1,2,3,…,1024 are written on a blackboard. They are divided into pairs. Then each pair is wiped off the board and non-negative difference of its numbers is written on the board instead. 512 numbers obtained in this way are divided into pairs and so on. One number remains on the blackboard after ten such operations. Determine all its possible values.Proposed by A. Golovanov combinatoricscombinatorics solvedinvariantParityblackboard