# This content is archived!

For the 2018-2019 school year, we have switched to using the WLMOJ judge for all MCPT related content. This is an archive of our old website and will not be updated.Mathematically find the last number. Since you are given the absolute distance from your guess to the answer, it is either above or below (positive or negative) the answer.

Let’s imagine the numbers on a number line. A is the answer, N_1 and N_2 are the guesses, and M_1 and M_2 are the respective distances from the answer.

We can derive the equation M = A − N. For which in the example above, M_1 is positive and M_2 is negative. There are four cases of combinations of positive and negative differences (M), but we don’t need to check them all. We just need to know if N_1 + M_1 = A.

Let us use some equations. If M_1 is positive, then N_1 + M_1 = A, otherwise, it wouldn’t. We can use a system of equations to check if M_1 is positive. \vert M_2\vert = A - N_2. We are given differences as absolute values, so the equation is equivalent to M_2 == A - N_2. Then we plug in A: M_2 = \vert N_1 + M_1 - N_2\vert. If the equation holds true, then M_1 is positive (output N_1 + M_1), otherwise, M_1 is negative (output N_1 - M_1).

## Time complexity

\mathcal{O}(1)