## Five makes 80 brainteaser

By David Shaw, 13 July 2022

Can you find 5 consecutive (counting upwards) numbers that add up to 80?

**Scroll down or click for a hint, or the answer!**

## Brainteaser hint

As a starting point, try:

80 ÷ 5 = 16

That means:

16 + 16 + 16 + 16 + 16 = 80

Next, think about how to make these consecutive numbers.

## Brainteaser answer

To start with, we can divide 80 by 5 to get 16. This reveals 5 equal numbers that add to 80:

16 + 16 + 16 + 16 + 16 = 80

To make them consecutive, we’ll need to subtract from some numbers and add to others. To keep the total the same, be sure to add and subtract the same amount.

To start with, try adding and subtracting 1. To fit the remaining numbers into the sequence, add and subtract 2:

(16 – 2) + (16 – 1) + 16 + (16 + 1) + (16 + 2) = 80

14 + 15 + 16 + 17 + 18 = 80

If you used a different method to solve this brainteaser, share your ideas below!

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27 July, 2022 at 2:39 pm

I solved it algebraically:

Let the first number be x. Then the subsequent numbers are x + 1, x + 2, x +3 and x + 4.

So x + x + 1 + x + 2 + x + 3 + x + 4 = 80

5x + 10 = 80

5x = 70

x = 14

So the numbers are 14, 15, 16, 17 and 18.

6 August, 2022 at 5:05 pm

I solved it by elimination.

Obviously it has to be numbers in the teens (e.g., any numbers starting with 2X * 5 is already much greater than 80). So, started with 12+…+16 and then 13, and then 14 to confirm that 14+15+16+17+18 = 80.