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Rule of Sum and Rule of Product

Seek simple and succinct solutions in these systems by sussing-out the significant symmetries.

Level 2

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When we write the integers from 1 to 100, how many times does the digit 9 appear?

Which of the following expresses the correct formula for the number of unit squares with exactly 1 red side in an \( n \times n \) square with \( n \geq 2 \) ?

Find the number of \(2\) digit numbers whose digit sum is a perfect square.

If you take a \(3 \times 3 \times 3\) Rubik cube and break it up into the \( 3^3 \) cubes, how many cubes would have stickers on exactly \(2\) faces?


Bonus question: Can you generalize this for a \(N \times N \times N\) Rubik cube?

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