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 enquired 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 four prices? (Do NOT count sales tax.)
(In reply to
re: a way to the solution by Charlie)
Hm.. yes, you are right, I overlooked a few things that still need to be dealt with.
0 1 5 5: The same argument as with 0 0 0 1: 711 is too big
5 5 5 6: Since I only used 5 and 6 to find two numbers of the solution, this set works just as well.
The numbers ending in 6: I wasn't looking hard enough outside the range of 75 - 319, because it is simple to show that all numbers of the solution have to be in that range:
For any number x in the solution, the following must be true:
((711-x)/3)^3 > 711000000/x
Otherwise the product of the remaining numbers can never be big enough. This is quite simple. (711-x) is the remaining sum for the 3 other numbers. This is divided by 3, and the result multiplied 3 times, as this will give the largest possible product for the given sum. The result is then compared to 711000000/x which is the target product for the last 3 numbers.
I won't solve this inequation now, it is simpler to just try out for which range of numbers it holds true.
Thanks for finding the holes in my solution so that I could try to fill them ;)
re(2): a way to the solution
