Ken's Puzzle of the Week

Central Tendency

I pulled out some old matchboxes from my cupboard and counted the number of matches in each.  The median, mode, and mean of these counts were respectively 3, 4, and 5.  What is the smallest number of matchboxes I could have found?

Stated differently, find a set of non-negative integers with the given measures of central tendency (median, mode, and mean) and the fewest number of elements.

Extension: Find sets (if possible) for each of the six assignments of {mean, median, mode} to {3,4,5}.  Repeat for {2,3,4}.


Source: Original.
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