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        riddles >> medium >> Arithmetic puzzle
        
(Message started by: Gerd on Mar 7^th, 2003, 1:29am)

Title: Arithmetic puzzle
Post by Gerd on Mar 7^th, 2003, 1:29am

Hello there! :)

I got a arithmetic puzzle (including the solution). My problem is, how can I solve such puzzles.
I would be very lucky, if someone could help me with my problem! :)

Here's the puzzle:
A customer at a 7-11 store selected four items to buy, and was told that the cost was $7.11. He was curious that the cost was the same as the store name, so he inquired as to how the figure was derived. The clerk said that he had simply multiplied the prices of the four individual items. The customer protested that the four prices should have been ADDED, not MULTIPLIED. The clerk said that that was OK with him, but, the result was still the same: exactly $7.11.
What were the prices of the four items?

Wish you a nice day :)

Title: Re: Arithmetic puzzle
Post by cho on Mar 7^th, 2003, 7:35am

In the CS forum there is a thread called 7-11 Riddle that shows you how to solve it with a computer program. If you want to solve it without a computer, it will take a little work.
First, as the other thread points out, it's easier to work with whole numbers, so you'll multiply each of your 4 items by 100, and you'll multiply 7.11 *100*100*100*100.
711=3*3*79
The remaining 3 100's add 6 2's and 6 5's as additional factors.
Your 4 items will have to be some combination of those 15 factors. That's a lot of possible combinations.
You'd best start by apportioning them as evenly as possible:
2*79=158
2*3*5*5=150
2*3*5*5=150
2*2*2*5*5=200
But that adds up to 658.
Now you just have to start shifting the numbers around until you find the right combination. I don't know of any way to lead you more directly to the right answer than that.

Title: Re: Arithmetic puzzle
Post by cho on Mar 7^th, 2003, 7:42am

I would add one other hint, that any time you move farther away from that even distribution, the total gets higher. So if your total is too low, move factors towards the extremes (for example, swap a 5 in one of the lower numbers with a 3 in one of the higher number to make the low lower and the high higher). If your total is too high, you have to get a couple numbers back closer to the average.

Title: Re: Arithmetic puzzle
Post by cho on Mar 7^th, 2003, 8:08am

One other thought: since 711 is odd, either one item or 3 items must have an odd price, so either one item is a multiple of 64, or you know exactly one item does not have 2 as a factor.

Title: :)Re: Arithmetic puzzle
Post by Gerd on Mar 7^th, 2003, 10:52am

Thanks a lot, cho! :)

I think that I'm fine with your guidance.
I got a couple of these puzzles (always only 1 solution). Now I can do it.

I wish you a nice day :)
Gerd

P.S. Sorry for my bad English. :(