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Problem 780

AMC 12 late, AIME early

Combinatorics Difficulty 4.3 Find the answer HMMT November

Compute the smallest positive integer that does not appear in any problem statement on any round at HMMT November 2023.

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

The number 22 does not appear on any round. On the other hand, the numbers 1 through 21 appear as follows. $\begin{array}{c|c|c} Number & Round & Problem \\ \hline 1 & Guts & 21 \\ 2 & Guts & 13 \\ 3 & Guts & 17 \\ 4 & Guts & 13 \\ 5 & Guts & 14 \\ 6 & Guts & 2 \\ 7 & Guts & 10 \\ 8 & Guts & 13 \\ 9 & Guts & 28 \\ 10 & Guts & 10 \\ 11 & General & 3 \\ 12 & Guts & 32 \\ 13 & Theme & 8 \\ 14 & Guts & 19 \\ 15 & Guts & 17 \\ 16 & Guts & 30 \\ 17 & Guts & 20 \\ 18 & Guts & 2 \\ 19 & Guts & 33 \\ 20 & Guts & 3 \\ 21 & Team & 7 \end{array}$

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.