# Blog

## Number cruncher

By

,

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!

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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## One response

1. Martin Towell

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.

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