Problems(1)
Let k be a positive integer. Determine the least positive integer n, with n≥k+1, for which the game below can be played indefinitely:Consider n boxes, labelled b1,b2,...,bn. For each index i, box bi contains exactly i coins. At each step, the following three substeps are performed in order:
(1) Choose k+1 boxes;
(2) Of these k+1 boxes, choose k and remove at least half of the coins from each, and add to the remaining box, if labelled bi, a number of i coins.
(3) If one of the boxes is left empty, the game ends; otherwise, go to the next step.Proposed by Demetres Christofides, Cyprus combinatoricsBMO