Question 657712: You have 10 bags of candy. Each bag contains 10 bars. 9 bags contain bars of 100 grams each. 1 bag contains bars of 90 grams each. How can you find which bag contains the 90 gram-candy bars with one weighing (you can use the scale one time only).
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Number the bags from 1 to 10. From each of the bags, take out enough candy bars so that the number of candy bars in the bag matches the number on the bag, i.e. take 9 out of bag 1, leaving 1, take 8 out of bag 2, leaving 2, and so on.
Weigh all of the bags. Subtract the total weight of all of the bags from 5500 grams and divide the result by 10. The answer will be the number of the bag with short weight.
The weight of 1 full weight candy bar plus 2 full weight candy bars plus...all the way up to 10 would be 100 plus 200 plus 300... plus 1000 equals 5500. The short weight bag is going to weigh 90x where x is the number of the bag, whereas all of the other bags are going to weigh 100 times the number of the bag. When you subtract the total weight from 5500, you get 10 times the number of the bag.
John
My calculator said it, I believe it, that settles it
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