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Magazine Problem 43
Draw a Hasse diagram for a partially ordered set that has two maximal elements and two minimal elements and is such that each element is comparable to exactly two other elements.
Problem 44
Draw a Hasse diagram for a partially ordered set that has three maximal elements and three minimal elements and is such that each element is either greater than or less than exactly two other elements.
Problem 45
Another problem attributed to ancient China is this: Fifteen pirates steal a sack of identical gold coins. When they try to divide them evenly, two coins are left over. A fight results in which one pirate is killed. The remaining pirates again try to divide the coins evenly, but this time one coin is left over. A second fight breaks out, and a second pirate is killed. When the remaining pirates again divide the coins, they find that each gets an equal number. Use the Chinese remainder theorem to find the smallest number of gold coins that could have been in the sack at the beginning.
