Question

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Easy interview question got harder: given numbers 1..100, find the missing number(s)

Hi guys, I wasn’t sure where to ask this but since this is an algorithmic question here it goes. I’ve come face to face with a math problem and can’t seem to get over it for the last couple of days. It goes like this:

You are given an adding machine that
sums a set of N+1 digits consisting of
positive integers 1 to N as it’s given
the numbers (e.g. the machine is given
3 as the first number and outputs 3.
It’s then given 6 as the second number
and outputs 9. It’s given 11 as the
third number and outputs 20. Etcetera
until it has processed N+1 numbers).
One (and only one) of the digits is
repeated. How do you determine which
number is repeated?

It seems like a trick question and I’d be really annoyed if it is just that a question to which the answer is ‘not possible’ – any ideas here?

Answer 1

Subtract (1+2+..+N) = N*(N+1)/2 from the sum.

EDIT: in case N is not known, find the largest triangular number smaller than the given sum and subtract.