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People of Brilliant, how are you all? I came across an interesting puzzle that I want some help solving.

Suppose we want to divide an equilateral triangle into \(n\) equal ...

\[1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 = 3^3 + 4^3 = 91.\]

Are there any other (non-trivial) sets of consecutive squares and cubes whose sums ...

This is the first edition of Left to the Reader - a monthly problem-solving blog written by the Brilliant team, including open-ended challenges for the community to solve and discuss. While ...

A random, 7-digit positive integer is selected. What is the most likely value for the sum of its digits?

Bonus: Generalize your answer to \(n\)-digit integers.

A monkey is typing a string of random letters, with all letters equally (and independently) likely to be typed.

Which word is more likely to appear first in the string ...

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