Difference between revisions of "2022 AIME I Problems/Problem 4"

Revision as of 17:33, 17 February 2022

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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+Write <math>i=e^{i\frac{\pi}{2}}</math>, it turns to: <math>\frac{\pi}{6}(3+r)=\frac{4n\pi}{6}</math>, so <math>3+r=4s+12k</math>
+it follows a pattern that <math>s=1,r=1,13....97</math> has 9 values; <math>s=2,r=5,17...89</math> 8 values and <math>s=3,r=9,21,...93</math> 8 values.
+So the answer is <math>33*(9+8+8)+9=834</math>
+~bluesoul