# A ----------y Puzzle

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Interpretation:

The title "A ----------y Puzzle":

A Probability Puzzle

The circles have ratio of areas 1:4 (and thus ratio of radii 1:2)

You flip the small circle (like a coin) and it lands completely inside the large circle, which has an inscribed equilateral triangle.

What is the probability of the small circle ...

intersecting ...

at least ... (L + EAST)

two edges of the triangle? (Microsoft Edge)

(See diagram below) The circle's centre lands uniformly at random within the inscribed (red) circle within the triangle. The purple lines are parallel to the triangle sides. The orange shaded area is where the circle's centre can land, while satisfying our condition.

Thank you Stiv for a brilliant disambiguation.

Trivia:

The size of the image is $$4361 \times 6449$$. Note that $$4369 = 7^2 \times 89$$ and $$6449$$ is a prime. Also, the size of the file is $$544333 = 3\times 7\times 25873$$ bytes.

• I'm pretty sure your second interpretation is the one that's almost correct, and that it's just rot13(Jung vf gur cebonovyvgl bs gur fznyy pvepyr vagrefrpgvat ng yrnfg gjb rqtrf bs gur gevnatyr? Gur 'nkvf' lbh zragvba vf cheryl n pbzcnff jvgu RNFG vaqvpngrq va erq gb svyy gur tncf nsgre gur Y sbe YRNFG.)
– Stiv
Dec 3, 2021 at 14:01
• Hahaha thank you that's brilliant. @Stiv Will change it. Dec 3, 2021 at 14:28
• Well done :) I was thinking of making it a bit more clear by adding a hint on how to interpret the circle inside the circle but you interpreted that (and almost everything else except the "east" part where Stiv helped out) exactly how it was intended which ofc leads to your answer. Dec 3, 2021 at 15:30
• @Prim3numbah thank you. I tried to go for the most natural interpretation at each step. Cool puzzle! By the way, are there any reasons for choosing the numbers in "Trivia" above? Dec 3, 2021 at 16:44
• @BenjaminWang Thanks! I see how you might think that was intentional, but no, completely unaware of those numbers. Not that obsessed with primes :D Dec 3, 2021 at 16:58