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### Identify The 4 Numbers

Identify The 4 Numbers - 4 April

Using the clues below, what four numbers am I thinking of?

The sum of all the numbers is 31.
One number is odd.
The highest number minus the lowest number is 7.
If you subtract the middle two numbers, it equals two.
There are no duplicate numbers.

1. 4 6 10 11

2. 12 8 6 5

3. explain how itz found out

4. You know that three of the numbers are even, and one is odd.
You know that the difference between the largest & smallest is 7; so one of them must be the odd number.
You know that the difference between the middle two is 2, so they must be consecutive even numbers.
You know all four are different.

So if x=the smallest & y=the 2nd smallest, you have
x+y+(y+2)+(x+7)=31, or 2x+2y=22, or x+y=11. Since we already know y has to be even, x is an odd number <11, and y is 11-x.

So the only possibilities are

1, 10 (,12, 8) = 31; but the difference between the largest (12) and the smallest (1) is 11, not 7. No good. How about
3, 8(, 10, 10) = 31; but 10 is duplicated. No good.
5, 6(, 8, 12) = 31, and it meets all the other criteria. Bingo?
7, 4(, 6, 14) = 31; but now x (7) isn't the smallest number, and that's true for x=9, the last possible value.

SO: the four numbers are 5, 6, 8, & 12.