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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



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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