Consider that you have n counters initialised with numbers $M_1 \dots M_n$. In each round you decrement exactly $k$ out of these counters. Keep doing this until at least $n-k+1$ counters are zero, so you can't continue. Determine the maximum number of rounds.
This can be illustrated with muffins, e.g. 18 nuts, 12 apple, 10 chocolate, 9 blueberry available. Form a maximum number of plates @ 3 different muffins each.
One can solve this with a greedy approach which always decrements the k largest counters. The proof that this is optimal is not hard but also non obvious.
My question is under what name this apparently rather natural question appears in the literature.