If you have 100 pills You have 10 bottles Each bottle weighs 1 gram You have 1 counterfiet it weighs 1.1 gram You can only use a scale to weigh one time Which one is the counterfit? Hint Number the bottles...
weigh one time?
Here is a method to weigh just a few times:
divide the bottles into two groups of five.
weigh each group, the heavy group cntains the culprit.
divide the heavy group into three sets, 2,2,1
compare the 2,2 group. If they areequal, the remaining bottle is bad.
If they are unequal, the heavy group of 2 contains the culprit.
compare those two.
To determine which bottle contains the counterfeit pill, you can follow these steps:
Step 1: Number the bottles from 1 to 10.
Step 2: Take 1 pill from bottle 1, 2 pills from bottle 2, and so on, up to 10 pills from bottle 10. This gives you a total of 55 pills.
Step 3: Now, weigh these 55 pills on the scale just once.
Step 4: If all the pills were genuine, the total weight should be (55 pills × 1 gram) = 55 grams.
Step 5: However, since one of the pills in the chosen set is counterfeit and weighs 1.1 grams, the total weight will be slightly higher if that specific set contained the counterfeit pill.
Step 6: Compare the measured weight with the expected weight. If the measured weight is higher than 55 grams, you can identify the bottle containing the counterfeit pill as follows:
- If bottle 1 was part of the chosen set, then the measured weight would be (55 grams + 0.1 gram).
- If bottle 2 was part of the chosen set, then the measured weight would be (55 grams + 0.2 grams).
- And so on...
By comparing the measured weight to the expected weight, you can identify the specific bottle that contains the counterfeit pill.
To identify the counterfeit pill using only the scale once, you can follow these steps:
1. Number the bottles from 1 to 10. This will help us keep track of each bottle.
2. Take 1 pill from the first bottle, 2 pills from the second bottle, 3 pills from the third bottle, and so on, until you take 10 pills from the tenth bottle.
3. Weigh all the pills taken together on the scale. The total weight should be the sum of 1 gram per pill (since each pill weighs 1 gram) and an additional 0.1 gram for the counterfeit pill (as it weighs 1.1 grams).
4. Now, subtract 55 grams (the total weight of the 1-10 pills) from the actual weight measured on the scale. The result will tell us which bottle contains the counterfeit pill.
5. For instance, if the measured weight on the scale is 56 grams, it means there is an extra 1 gram in the mix, indicating that the counterfeit pill is in the first bottle (because only the pills from the first bottle contribute to the additional weight).
By following this method, you can determine the bottle containing the counterfeit pill using just one weigh-in on the scale.