# Mistake at the Apple Farm Puzzle - Solution

### The Puzzle:

Someone has mixed up the apples. Read carefully what has happened. Can you find a way to help solve the problem.

- There are 10 baskets containing apples.
- There are various amounts of apples in each basket ranging from 10 to 20.
- 9 of the baskets have apples weighing 4 ounces each.
- 1 of the baskets has apples weighing 5 ounces each.
- All the apples look the same.
- The equipment you have is a set of scales and an empty basket.
- It is late and the truck is waiting to take the apples to market. You only have time to make one measurement using the scales.

### Our Solution:

It could work something like this:

Number Each Basket from 1 to 10.

Select 1 Apple from basket 1

Select 2 Apples from basket 2

etc..

You will now have (1+2+...+10) = 55 Apples

If they all weighed 4 oz, then the scales would show 55x4=220 oz.

But if the weight was, say, 225 oz, then you would know that there 5 apples that weigh an extra ounce, so the basket with the heavier apples must be basket 5.

Number Each Basket from 1 to 10.

Select 1 Apple from basket 1

Select 2 Apples from basket 2

etc..

You will now have (1+2+...+10) = 55 Apples

If they all weighed 4 oz, then the scales would show 55x4=220 oz.

But if the weight was, say, 225 oz, then you would know that there 5 apples that weigh an extra ounce, so the basket with the heavier apples must be basket 5.

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