# The Happy Farmer

**Discrete Mathematics**Level 2

A farmer sold his grain in 40 pound sacks because his only scale was a simple balance using a rock weighing exactly 40 pounds. One day the rock dropped and broke into 4 pieces. The farmer took the pieces of rock to the dealer where he had purchased the scale to see if they could be glued back together. The dealer weighed the four pieces and told the farmer that his grain could now be weighed in 1 pound increments all the way up to 40 pounds using the pieces of rock in various combinations on each platter. The farmer was overjoyed!

How much does each of the 4 pieces of rock weigh in order to make that possible?

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