A deck of 2n\plus{}1 cards consists of a joker and, for each number between 1 and n inclusive, two cards marked with that number. The 2n\plus{}1 cards are placed in a row, with the joker in the middle. For each k with 1≤k≤n, the two cards numbered k have exactly k\minus{}1 cards between them. Determine all the values of n not exceeding 10 for which this arrangement is possible. For which values of n is it impossible? invariantcombinatorics proposedcombinatorics