## Thursday, May 25, 2006

### Going to the Orchard

The local orchard has a strange pricing structure. Each bag holds seven apples for which they charge five cents. If you want an eighth apple, you get charged 15 cents. So, if you want to buy 23 apples, you would have to pay 15 cents for three bags and 30 cents for the remaining two for a total of 45 cents.

My question is which costs more: 10 apples, 30 apples or 50 apples?

There's no real puzzle or hard math here, but the answer may surprise you.

1. they all cost the same

neat!

2. Ooh that was weird. They all cost the same: 50 cents.

3. And 70 also cost the same. But there is a big jump for 90.

Likewise, 6, 26, 46, 66, 86, 106, and 126 all cost the same.

When you add 20 apples, you are adding 3 bags, but taking away one single (so +3*5¢ - 15¢), sunless you have a multiple of 7 already, in which case you add 2 bags and 6 singles.

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