Enigma 1290: Marbled patterns
29 September 2014
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From New Scientist #2448, 22nd May 2004 [link]
I laid out a row of identical saucers and gave my nephew some marbles, all the same. I then set him the following problem:
“If I ask you to place all the marbles in the saucers, with at least one marble in each, in how many ways can this be done?”
After some thought he came to the correct conclusion that there were between a thousand and ten thousand such arrangements, and then he gave up. So I then asked him the following simpler question:
“How many of these arrangements will be symmetrical, in the sense that if I reversed the order of the saucers the pattern remains the same?”
This time he gave the correct answer of 20.
What was the correct answer to the first question?
Note: I am waiting for a phone line to be connected at my new house, so I only have sporadic access to the internet at the moment.