There are 8 bags each containing 10 gold coins In 7 of the b

There are 8 bags, each containing 10 gold coins. In 7 of the bags each coin is 10 ounces. In one of the bags each coin is 11 ounces. How is it possible, in a single weighing on an accurate weighing scale to determine which bag contains the 11 ounce coins? Possible Bonus: What is the answer? What type of problem is this _____?

Solution

Here we mark each bag as A,B,C,D,E,F,G and H. Now we take 1 coin from first bag , 2 coins from second bag, 3 coins from third bag and so on and put all of them on the scale, so that their sum

= 1+2+3+4+5+6+7+8 = 36

And their total weight = 36 x 10 = 360 ounces.

But if one bag has coins with 11 ounces, so when that bag`s coins will be added, the extra weight will be shown on the scale and thus obtained total weight is noted and then we subtract 360 ounce from that shown weight that scale shows when 11 ounces coin are put on it.

The difference between two readings will tell us the right bag as if the difference is 1 ounce, the required bag will be bag A, if difference is 2 ounce, the required bag will be bag B, if the difference between two readings is 3 ounce, the required bag will be bag C and so on.

In this way we can detect the required bag.

Answer

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Such problem is classified as weight problems.