Simply Insane?
Level
pending
X + Y = ?
X - Y = ?
XY = ?
X/Y = ?
All 4 question marks above are positive integers from 1 to 16, but no 2 of them are the same.
Hence, find the largest positive integer being used.
9
12
13
10
16
15
14
11
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1 solution
Firstly, notice that X = (? + ?)/2 by the first 2 statements. This means X is either ending with '.0' or '.5'.
If X is ending with .0, Y must be ending with .0 too. If X is ending with .5, Y must be ending with .5 too.
But if both X and Y end with .5, the multiplication result cannot be a positive integer. So we now know both X and Y are integers.
Both X and Y cannot be negative integers, or else the addition result cannot be a positive integer. If either X or Y is a negative integer, the multiplication result cannot be a positive integer. So we now know both X and Y are positive integers.
It is clear by the last statement that X is a multiple of Y. However, Y cannot be 1, or else both the multiplication and division result will be the same. So Y is at least 2.
If X and Y is 2, the addition and multiplication result will be the same.
If X is 4 and Y is 2, the subtraction and division result will be the same.
If X is 6 and Y is 2, the problem is solved.
What happens if Y is 3?
If X and Y is 3, the subtraction result will be 0, which is not allowed.
If X is 6 and Y is 3, the multiplication result will be 18, which is not allowed.
If X and Y is 4, the subtraction result will be 0, which is not allowed.
For other cases, the multiplication result is not allowed.
Hence, there is only 1 solution: X = 6, Y = 2.
6 + 2 = 8
6 - 2 = 4
6 x 2 = 12
6 / 2 = 3
The largest positive integer being used is 12.