Dorothy and Toto were bringing to market the weekly eggs laid by Aunt Em’s hens. Leaving an intersection when the light turned green, Dorothy accelerated too fast and the crate of eggs fell off the back of the truck. All of the eggs broke. Traffic was snarled up for awhile. Dorothy explained to an inquisitive police officer that she hadn't counted the eggs (Em had done that, of course), but she estimated that there were between 50 and 100 to begin with. You are not part of this story, but you can find the exact number if you know, improbably, that if the eggs were counted by two’s, there would be none left over. Likewise if they were counted by three’s. But when counted by five’s, there would be three left over. How many eggs were there in Dorothy’s truck before they fell out of it?
Solution
If n is the number of eggs, then n is a multiple of 6 between 50 and 100, in other words, n is either 54, 60, 66, 72, 78, 84, 90, or 96. The only one of these that leaves a remainder of 3 when divided by five is 78. So seventy-eight it is. Or was.