### Brain Teasers

# Discount Policy

The local CD shop operates an unusual discount policy. The discount on the next purchase is worked out on the current purchase in the following way: for every whole dollar spent you get 0.5% discount on the next purchase. For example, if you purchased $8.99 on the first purchase, you would then get a 4% discount on the next purchase and so on. You can make as many purchases as necessary.

You need to buy 7 CDs, costing, $11.50, $12.00, $12.00, $12.50, $13.00, $13.00 and $14.50 - what is the cheapest method of buying them?

You need to buy 7 CDs, costing, $11.50, $12.00, $12.00, $12.50, $13.00, $13.00 and $14.50 - what is the cheapest method of buying them?

### Hint

Make 2 purchases.### Answer

Purchase 1: $11.50, $12.00, $12.00, $12.50 = $48.00 (which gives a 24% discount on the next purchase).Purchase 2: $13.00, $13.00, $14.50 = $40.50 minus 24% discount = $30.78. For a total cost of $78.78 dollars.

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## Comments

Excellent teaser.

Thank you very much!

I am currently reading over all of my teasers, and Princess_Neopia, your comment was made a year ago! Wow, this year sure has gone by quickly. Happy 2004 to all!

Given the high number of purchase combinations possible, I'm curious if there's some simple way to prove that this is the least expensive way to do it.

By trial-and-error, I figured out that you get the cheapest price by buying half the first day, and half the second. You can't evenly split 7 prices in half, but the given answer is the closest you can get, and therefore the cheapest. Great teaser!

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