Given 10 identical bottles of identical pills (each bottle contains 100 pills). Out of 10 bottles 9 have 1 gram of pills but 1 bottle has pills of the weight of 1.1 gram. Given a measurement scale, how would you find the heavy bottle? You can use the scale only once.
Question
Given 10 identical bottles of identical pills (each bottle contains 100 pills). Out of 10 bottles 9 have 1 gram of pills but 1 bottle has pills of the weight of 1.1 gram. Given a measurement scale, how would you find the heavy bottle? You can use the scale only once.
Solution
Sure, here is the solution:
- Number the bottles from 1 to 10.
- From each bottle, take a number of pills corresponding to its number (i.e., from bottle number 1, take one pill; from bottle number 2, take two pills, and so on).
- Put all these pills together and weigh them.
- The total weight should be 55 grams if all pills are 1 gram each. However, because one bottle contains 1.1 gram pills, the total weight will be more than 55 grams.
- The difference between the total weight and 55 will give you the number of the bottle with the heavier pills. For example, if the weight is 55.3 grams, then the bottle number is 3 because you took 3 pills from the 3rd bottle.
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