Question

Suppose you write 10 consecutive natural numbers on a board. When one of the numbers is erased, the sum of the remaining numbers is 2015. What number was erased?

Answer 1

220

Explanation:

If there are 10 numbers that add up to a sum, and one removed leaves a total of 2015. Then 9 numbers add up to 2015. If the sum of 9 numbers is equal to 2015, by dividing 2015 by 9, we get the mean which is an approximate of 223.8

If we add numbers to either side of 223, until we have 10 numbers in total resulting in either

219+221+220+222+223+224+225+226+227+228 : Equation 1

or

218+219+221+220+222+223+224+225+226+227 : Equation 2

However when we add them up, Equation 1 sums to 2235, and Equation 2 sums to 2225.

Looking at Equation 1, in order to get from 2235 to 2015 by removing 1 number, we do 2235-2015=220, and we see that 220 is within the sequence so it is a valid answer.

If we do 2225-2015 for Equation 2 though, we get a difference of 210, which is not in that sequence.

Therefore the sequence of numbers, is that of Equation 1, and by removing 220 from that sequence, we get 9 numbers summing to 2015.

Hope this helps!