Suppose you have 10 boxes and each box contains 10 Cigarettes.
- 9 out of 10 boxes have each Cigarette of 10 gm.
- Remaining 1 box has each Cigarette of 11 gm.
The task is to find the box which contains 11gm Cigarettes.
Constraint:
- You have an electronic weighing machine and with the help of that you have to identify the box which contain 11 gm Cigarettes.
- You can use the weighing machine only once.
Solution:
Take 1 Cigarette out from box 1.
Take 2 Cigarettes out from box 2.
Take 3 Cigarettes out from box 3.
Take 4 Cigarettes out from box 4.
Take 5 Cigarettes out from box 5.
Take 6 Cigarettes out from box 6.
Take 7 Cigarettes out from box 7.
Take 8 Cigarettes out from box 8.
Take 9 Cigarettes out from box 9.
Take 10 Cigarettes out from box 10.
Now weigh all taken out Cigarettes on weighing machine. The sum of weight for each boxes is 1*10+2*10+3*10+4*10+5*10+6*10+7*10+8*10+9*10+10*10 = 550 gm.
But as 1 out of 10 boxes has Cigarettes of 11 gm, weight on weighing machine will be (550 + k) gm.
And here k will be our box number which contains 11 gm Cigarettes.
Example: Suppose box number 4 has 11 gm Cigarettes and all other boxes have 10 gm Cigarettes. Therefore, weight on weighing machine will be:
1*10 + 2*10 + 3*10 + 4*11 + 5*10 + 6*10 + 7*10 + 8*10 + 9*10 + 10*10 = 554 gm = 550 + (4) and this 4 is our required box number which has 11 gm Cigarettes.
This means that if the weight on the weighing machine is (550+k) gm, 1 ≤ k ≤ 10.
k will be our required box number which contains 11 gm Cigarettes.