# Blog

## Five makes 80 brainteaser

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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.

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.

(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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## 2 responses

1. Karen

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.

2. Sam

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.

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