The Mind of a Marksman
In a shooting match, 8 clay targets are arranged in two hanging columns of three each and one column of two. A marksman must break all targets according to the following rules: (1) The marksman first chooses a column. (2) The marksman must then break the lowest unbroken target in the chosen column. If these rules are followed and the marksman never misses, in how many different orders can the targets be broken?
The answer is 560.
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1 solution
There is a one-to-one correspondance with the arrangments of A A A B B C C C which is 3 ! 3 ! 2 ! 8 ! = 5 6 0 .