Subtract from 2018
From , subtract half of it first. Then subtract rd of the remaining number , then subtract th of the remaining number and so on until th of the remaining number is subtracted.
What is the remaining number?
The answer is 1.
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Start off with x 1 = 2 0 1 8 . If we take away half of this, we obtain x 2 = x 1 − 2 1 x 1 = 2 2 0 1 8 If we now take away one third of this, we obtain x 3 = x 2 − 3 1 x 2 = 3 2 0 1 8 In general, after we have taken away one j th of the previous number, we are left with x j = x j − 1 ( 1 − j 1 ) = j 2 0 1 8 Thus, at the end, we are left with x 2 0 1 8 = 1 , making the answer 1 + 1 = 2 .