Math CentralQuandaries & Queries


Question from Megon, a parent:

Of the 24 four-digit numbers formed from the digits 1,2,3,&4 is there an easier way to find their sum other than writing them all out and totaling them by hand?

Hi Megon.

Sure. Total up the units digits. Each of the four digits 1, 2, 3 and 4 appears six times, so adding the units digits is equivalent to

6(1) + 6(2) + 6(3) + 6(4) = 6(10) = 60.

If the units digits add to 60, then what about the 10's digit and so on?

Hope this helps,
Stephen La Rocque.

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