MathDB

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 \leq k \leq 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?

Problem Statement