OlympiadMediumCombinatorics7–9

Adding Up Every Rearrangement

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All the four-digit numbers whose digits are $1$ , $2$ , $3$ and $4$ in some order, each digit used exactly once, are written down. What is their sum?

Count how often a given digit lands in the units place, and note that the count is the same for every digit and every place.

Solution

Step 1 of 5