Weights

From the Tournament of the Towns:

A balance and a set of metal weights are given, with no two the same. If any pair of these weights is placed in the left pan of the balance, then it is always possible to counterbalance them with one or several of the remaining weights placed in the right pan. What is the smallest possible number of weights in the set?

Solution

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Laundry

A stunner from the Baltic Way:

A family wears clothes of three colours: red, blue and green, with a separate identical laundry bin for each colour. At the beginning of the first week, all the bins are empty. Each week, the family generates 10kg of laundry (the proportion of each colour might vary week to week). The laundry is sorted by colour and placed in the bins. Next, the heaviest bin (only one if there are several) is emptied and its contents washed.

What is the minimum requirement (in kg) of each bin?

Solution

The Coin Collection

A PuzzleCritic Original:

The Museum of Mathematical Mysteries houses a peculiar collection of coins, each shaped like a polygon, with the two largest proper factors of n inscribed on either face, where n is the number of edges the given coin possesses. For example, there is a hexagonal coin on which the numbers 2 and 3 are inscribed. The museum’s curator examines one of the coins and sees the number 15 inscribed on one face. Determine all numbers that might appear on the other face.

Solution