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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

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## Comments

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TopNewestNumber of months with $29 , 30$ and $31$ days in $1001$ leap years.

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Wow that's quick!

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Thanks.

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awesome...

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Genius!

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Cool observation Sir!

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amazing !

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Take $x=1$ and by Chicken McNugget there exists $y,z$ such that $30y+31z=366337$.

That's the most straightforward way that immediately solves the problem as far as I know.

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But Chicken McNugget didn't explicitly say that $y,z$ are positive.

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It does; or else it would just degenerate to Bezout's Identity.

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x=3955;y=4078;z=4171

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x=3955;y=4078;z=4171;

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see if HCF of 29,30,31 divides 366366 completely

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Won't HCF of $29$, $30$ and $31$ be $1$?

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