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2022 AIME I Problems/Problem 4

Revision as of 16:34, 17 February 2022 by Bluesoul (talk | contribs)

solution 1

Write $i=e^{i\frac{\pi}{2}}$, it turns to: $\frac{\pi}{6}(3+r)=\frac{4n\pi}{6}$, so $3+r=4s+12k$

it follows a pattern that $s=1,r=1,13....97$ has 9 values; $s=2,r=5,17...89$ 8 values and $s=3,r=9,21,...93$ 8 values.

So the answer is $33*(9+8+8)+9=834$

~bluesoul

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