2020 USOJMO

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Shh..., don't tell anyone (giving you 2 free jmo problems!) (solutions for 2020 USOJMO)

Problem 1: $8^8$ = $2^x$. Find x.

Solution: $8^8 = 2^24$ so x = $\boxed{24}$

Problem 2: Bob eats 1 hamburger a day. He likes to eat his hamburgers by putting the whole thing in his mouth. After how many days will he eat exactly 1.7 hamburgers?

Solution: He will never eat the amount of burgers because he always eats 1 at a time in one go. Thus, the answer is $\boxed{0}$.