Chinese Restaurant Party

At a large party in a Chinese restaurant (Wok Around the Clock), every three guests used a bowl of rice among them, every four guests used a bowl of soup among them, and every pair of guests used a bowl of fish between them. There were 65 bowls of these three things altogether. How many guests were at the party?

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Marble Piles

Jasper had his marbles out on the floor the other day. His little sister Pearl was putting them in equal piles, or trying to. When she tried to put them in two equal piles, she had one marble left over. When she tried to make three equal piles she had two marbles left over. When she tried to make four equal piles, she had three marbles left over. Then she got mad and threw all of the marbles under the piano. Jasper pulled them all out (he didn’t lose any, and he kept his temper) and put them into seven equal piles, with no marbles left over. How many marbles does he have?

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Super-Venn (Sums in Circles)

The following diagram is composed of 10 overlapping circles, each identified by a letter. Each letter has a different whole number value from 1 through 9; since there are two circles labeled H, H will have the same value for both circles. Where some circles overlap, there is a number indicated: This number is the sum of the values of the letters in the overlapping circles. Can you figure out the correct numerical value for each letter?

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The Problem Before… After…

Answer this question yes or no: If the problem you solved before you solved the problem you solved after you solved the problem you solved before you solved this one, was harder than the problem you solved after you solved the problem you solved before you solved this one, was the problem you solved before you solved this one harder than this one?

Show how you decided.

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