A code consists of either a single letter or a pair distinct letters in alphabetical order to identify each participant. What is the least number of letters that can be used if there are 12 participants and each participant is to receive a different code?

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Official Explanation

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Let's take it this way: if we take 4 letters A, B, C, D, then we can have 4 single-letter codes, and 6 double-letter codes (AB, AC, AD, BC, BD, CD).

That gives a total of

4 + 6 = 10

codes, which is insufficient for 12 participants.

If we take 5 letters, the number of single-letter codes is 5, and the number of distinct pairs in alphabetical order is the number of combinations of 2 letters from 5, which is inom{5}{2} = 10.…

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What this question tests

What it tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Common trap

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.