Question

There are 10 stacks of 10 coins each. 9 of the stacks contain coins that weigh 1g each. The other stack contains coins of 2g each. The coins look the same. We have a scale that we can get a measurement of grams from, not a balance. We can use the scale exactly once to weigh anything here from a single coin to all of them. How can we determine which stack is the 2g coins?

Answer 1

Since we have only one chance of measuring, we form a special set of coins and measure this set.

we take 10 coins from stack 1

9 coins from stack 2

8 coins from stack 3

7 coins from stack 4

6 coins from stack 5

5 coins from stack 6

4 coins from stack 7

3 coins from stack 8

2 coins from stack 9

1 coins from stack 10

If all the set have 1 gm coin then total weight would have been = 55

But since one stack contains 2 gm coins so the actual weight will tell from which stack they are taken.

for example if total weight = 65 gms

then extra weight = 65-55 = 10 gms which corresponds to stack 1

if total weight = 64 gms

then extra weight = 64-55 = 9 gms which corresponds to stack 2

and so on.