## Paying the miller brainteaser

By David Shaw, 2 June 2022

**Difficulty: Tricky**

A farmer goes to the local mill to get some wheat ground into flour. The miller doesn’t ask for money – instead, they take one tenth of the wheat as payment.

If the farmer wants 100 kilograms (kg) of flour at the end, how much wheat should they bring?

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

## Brainteaser hint

Remember to check your answer. Work out how much the miller will take and subtract it from your suggested amount. The farmer might end up with less than you’d hoped!

## Brainteaser answer

A good first guess is to start with 100 kg, and then add one tenth, or 10 kg more to get 110 kg.

However, if you take 110 kg to the mill, the miller will take 11 kg leaving you with only 99 kg! If you add another kilo to cover that, the miller will take another 100 grams to grind that extra kilo. And if you add another 100 grams, the miller will take 10 more grams and so on.

In the end, you’ll need to bring 111.111,111,111,111,111… kg. If you’re in high school, you might know how to turn this number into a mixed fraction: 111 1/9 kg.

To be safe, you could also simply round up and bring 112 kg!

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10 June, 2022 at 12:51 pm

The fraction at the end should be 1000/9. To solve I set up the equation: x-0.1x=100 and solve for x. So 0.9x=100 or x=100/0.9

10 June, 2022 at 1:41 pm

Ooh! I meant to say that 111 1/9 is the answer expressed as a mixed fraction. Thanks for the catch!