#1 How many positive perfect cubes divide (3!)(5!)(7!)? (Source: with hints and solutions —MAA Minute Math)
#2 A new assistant accidentally left open the cages at the pet shop, and over 100 birds escaped There were exactly 300 birds to begin with. The next morning, the local newspaper carried a report that gave the following figures:
“Of the birds that remained, a third were finches, a quarter were budgies, a fifth were canaries, a seventh were mynah birds, and a ninth were parrots.”
However, the reporter got one of the fractions wrong. How many parrots were left? (Source: Devlin’s Angle, by Keith Devlin)
Let me know if you have thoughts on these.