Dorothy Eggs

Dorothy and Toto were carefully driving their small veggie-oil-powered truck containing three baskets of eggs to market, when a car going at full speed collided with the truck. Dorothy was unhurt, but Toto got a broken leg. The eggs were destroyed. The car’s driver admitted his responsibility and offered to pay for the eggs. Dorothy said he must pay Toto’s vet bill too. The driver, aghast, asked, “Toto too?” Dorothy compromised and said she’d pay half the vet bill if the driver could answer a simple problem for her:

The number of eggs was somewhere between 50 and 100. If they were counted out 2 at a time or 3 at a time, none would remain at the end. But if they were counted out 5 at a time, there would be 3 left over.

The driver was required to say how many eggs there had been in the baskets. What answer would get him off the hook for the full vet bill?

Show/Hide Solution

Since the number of eggs is divisible by both 2 and 3, it is a multiple of 6. The multiples of 6 between 50 and 100 are: 54, 60, 66, 72, 78, 84, 90, and 96. We see that 78 is the only possibility that is 3 more than a multiple of 5, so there must have been 78 eggs.

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