## Number cruncher

By David Shaw, 28 November 2018

I have four different whole numbers written on a piece of paper.

- The largest number is four bigger than the smallest.
- The middle two numbers are even.
- If I add all four numbers together, I get 12.

What are my numbers?

Scroll down for the answer!

## Brainteaser answer

You might think there are lots of possibilities to check, but there are some tricks to make the puzzle easier.

First, a quick estimate of how big the numbers are. There are four numbers and they add up to 12. Since 3 + 3 + 3 + 3 = 12, the four numbers you’re looking for should average about 3.

The difference between the smallest and largest numbers is four, so the biggest number can be written as: smallest + 4.

There are only three possible numbers between the smallest and largest numbers: smallest + 1, smallest + 2, and smallest + 3.

Since the two middle numbers are even, they must be two apart. So the two middle numbers must be smallest + 1 and smallest + 3.

Time to try some numbers! If you make the smallest number 1, then you get 1, 1 + 1, 1 + 3 and 1 + 4. Calculating them out, you get 1, 2, 4, and 5. They add up to 12, so that’s the correct answer!

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28 November, 2018 at 4:25 pm

Rather than trial and error as the last step, you can add all those numbers up (I’ll use “S” instead of “Smallest” to make it easier on the typing)

(S) + (S+1) + (S+3) + (S+4)

= 4S + 8

We know this totals 12, so

4S + 8 = 12 (subtract 8 from both sides)

4S = 4 (divide both sides by 4)

S = 1

Then you can get the other numbers by just adding 1, 3, and 4 to that.