10 identical bottles of pills | Puzzles for Interview - Interview Preparation PDF Download

Introduction

In this puzzle, we have 10 identical bottles of pills with each bottle containing 100 pills. Out of these 10 bottles, 9 bottles have pills weighing 1 gram each, but 1 bottle has pills weighing 1.1 grams each. We need to identify the bottle with heavy pills using a measuring scale, but we can only use the scale once.

Solution

Step 1: Arranging the Bottles
The first step is to arrange all the bottles on the shelf. We need to number the bottles from 1 to 10. Then, we need to take 1 pill from the first bottle, 2 pills from the second bottle, 3 pills from the third bottle, and so on, until we take 10 pills from the tenth bottle.

Step 2: Weighing the Pills
Now, we need to weigh all the pills we have collected. Ideally, we should have a total of (10) x (11)/2 = 55 pills, weighing 55 grams. When we put all the pills on the measuring scale, the deviation from 55 grams will tell us which bottle has the heavy pills.

Step 3: Identifying the Heavy Bottle
If the deviation from 55 grams is 0.1 grams, the first bottle has the heavy pills. If the deviation is 0.2 grams, the second bottle has the heavy pills, and so on. For example, if the deviation is 0.3 grams, then the third bottle has the heavy pills.

Conclusion

In conclusion, we can identify the bottle with heavy pills by arranging the bottles, taking pills from each bottle, and weighing them on a measuring scale. We can only use the scale once, so we need to be careful while weighing. By following these steps, we can solve this puzzle and identify the bottle with heavy pills.