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The Discount is a puzzle in Professor Layton and the Unwound Future.

Puzzle

US Version

This shop only sells three different items for one, two, or three pounds. If you buy two of the same item, you can buy a third of that item at half price.

You bought six items and paid 9.5 pounds. How many of each one-, two-, or three- pound item did you buy? You bought at least one of each, and there's no tax.

UK Version

This shop only sells items that cost £1, £2 or £3.
If you buy two of the same item, you can buy a third one at half price.

You bought six items and paid £9.50. How many £1, £2 and £3 items did you buy? You bought at least one of each.

Line up the items from left to right to show how much of each one you bought.

Hints




Click a Tab to reveal the Hint.

In the total amount that you paid, there's a fraction.

Start your line of thinking from there.

The half-price items that result in a fraction are the one-pound and three-pound items. Remember the conditions for getting the half-off discount.

If you but three of the three-pound items, you'll exceed 9.5 pounds if you try to buy a total of six items. The item that gives you the 0.5 is the one-pound item.

Your shopping total is 9.5 pounds. If you don't buy at least three of the same item, you won't get that 0.5 pound. If you buy three of the one-pound item, you get a total of 2.5 pounds. You still need to buy seven pounds' worth of items, so think hard.


Solution

Correct

Splendid!

US Version

You bought three one-pound items, two two-pound items, and one three-pound item. To get the 0.5 pounds, you have to buy three of either the one-pound or three pound item. But you knew that already, didn't you!

UK Version

You bought three £1 items, two £2 items, and one £3 item. To get the last 50p, you'd have to have bought three of either the £1 or the £3 items - though the latter option would have taken you over budget. But you already knew that, didn't you?

UF088S

A big thanks to http://professorlayton3walkthrough.blogspot.com