We have 10 bags of 1 Rupee coins. One bag contains all the defective coins, the weight of each coin in that bag is 1 gram lesser than the weight of a normal 1 Rupee coin. You have a spring balance, which tells the exact weight. After how many minimum no. of weighs you can separate the bag with defective coins.
Other variant of the same problem:
There are 10 machines in a factory. Each produces coins weighing 10 grams each. One day the factory owner cones to know that one of the machine is not functioning properly and produces coins of weight 9 grams. You have to find out the faulted machine. You ONLY have a weighing machine and you can use it only ONCE.
Want to try now ?
Let P is the no. of the bag which contains the defective coins.
Then S = (W grams)*(1+2+3….+10) – P*(1 gram)
P will come out to be a number between 1 to 10 and thats the required bag.
River crossing – the harder one