Find the box which contains Box of 11 gm Cigarettes | Puzzles for Interview - Interview Preparation PDF Download

Introduction

Suppose you have ten boxes, each containing ten cigarettes. Out of these ten boxes, nine boxes have each cigarette weighing 10 grams. However, one box contains cigarettes that weigh 11 grams. The challenge is to identify the box that has 11 gm cigarettes, using an electronic weighing machine. You have only one chance to weigh the cigarettes.

Step-by-Step Solution

1. Take one cigarette from the first box, two from the second box, three from the third box, and so on, until you take ten cigarettes from the last box.
2. Weigh all the taken out cigarettes on the electronic weighing machine.
3. Calculate the sum of the weights for each box, which will be 1*10 + 2*10 + 3*10 + ... + 10*10 = 550 gm.
4. As one box has cigarettes weighing 11 gm, the total weight on the weighing machine will be (550 + k) gm, where k is the box number that contains the 11 gm cigarettes.
5. For example, if box number 4 has 11 gm cigarettes, and all other boxes have 10 gm cigarettes, the total weight on the weighing machine will be 1*10 + 2*10 + 3*10 + 4*11 + 5*10 + ... + 10*10 = 554 gm. This weight is equal to 550 + 4, which means that box number 4 has 11 gm cigarettes.
6. Therefore, if the weight on the weighing machine is (550 + k) gm, where 1 ≤ k ≤ 10, then box number k contains 11 gm cigarettes.

Conclusion

By following these steps, you can easily find the box that contains 11 gm cigarettes. This puzzle requires logical thinking and basic math skills. It is a fun way to exercise your brain and improve problem-solving abilities.