Picky arithmetic progression
Probability
Level
3
What is the total number of ways in which three distinct numbers in an arithmetic progression can be selected from the numbers 1 to 24 inclusive?
The answer is 132.
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1 solution
Clever problem!
The lowest and the highest term of the A.P. will both be even or they will both be odd. To build an A.P with even end terms we choose 2 numbers out of the 12 even numbers in our range, giving us ( 2 1 2 ) options; the middle term is then given as the average of the end terms. We can build just as many sequences with odd end terms, for a total of 2 ( 2 1 2 ) = 1 3 2 .