# Marble weight riddle

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There are 10 bags, filled with marbles. The number of marbles in each bag differs, but all bags contain ten marbles or more. Nine of the ten bags only contain marbles of 10 grams each. One bag only contains marbles of 9 grams. In addition, you have a balance which can weigh in grams accurate, and you are allowed to use it only once (i.e. weigh a single time).

How can you find out in one weighing, which bag contains the marbles of 9 grams? First of all..
Let us assume that all 10 bags contain marbles weighing 10gms each..
so if you take 1 marble from the first bag
2 marbles from the second bag
3 marbles from the third bag
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10 marbles from the tenth bag
The total weight when measured will be (10+20+30+40+…..100)=  550gms
BUT ,
one of the bag contains marbles which are 9gms each……
so  in case if it was from the first bag ,when you  weigh  = ( 9+20+30+….100)=549gms
if it was from the second bag,                                      (10+18+30+40+….100)=548gms
if it was from the third bag,                                          (10+20+27+40+…..100)=547gms
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similarly you can find which is the defective one by weighing only once.