Exclude One
Algebra
Level
2
A teacher writes six consecutive integers on a blackboard and then erases one of them. The remaining five add up to 2018.
What was the one erased?
The answer is 403.
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1 solution
a + 0 , a + 1 , a + 2 , ⋯ a + 5 are 6 consectives integers. Since sum of 5 of them = 2 0 1 8 5 a + x = 2 0 1 8 ⟹ a = 5 2 0 1 8 − x we note that sum of 5 cosecutives integers is 1 5 and possible of value of x = 1 3 = 0 + 1 + 3 + 4 + 5 . Hence we find a = 4 0 1 and erased number is a + 2 = 4 0 1 + 2 = 4 0 3 .