Track / Stage 4 / 256 of 340 #516 of 2000

Problem 516

AMC 12 late, AIME early

Combinatorics Difficulty 4.9 Find the answer HMMT_2

Count the number of sequences $a_{1}, a_{2}, a_{3}, a_{4}, a_{5}$ of integers such that $a_{i} \leq 1$ for all $i$ and all partial sums $\left(a_{1}, a_{1}+a_{2}\right.$ , etc.) are non-negative.

Your answer

Official solution

$C$ (length +1 $)=C(6)=132$ .

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