IBM Ponder This #003 · July 1998

After Wimbledon, the remaining tennis balls are to be placed in buckets. There are $k$ rows of buckets, with three buckets in every row and therefore $3k$ buckets in total.

Assign a different positive integer to every bucket so that the three bucket counts in every row have the same total. Among all such arrangements, make that common row total as small as possible.

For example, when $k=2$, six distinct bucket counts can achieve a common row sum of $11$.

For an arbitrary number of rows $k$, construct an arrangement that always attains the minimum possible common row sum.

Solution

Best opened after a real attempt

Solution

To be added.