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You have 5 pill bottles; 4 bottles contain 10 x 10mg pills, and 1 bottle has 10 x 9mg pills. You have digital scales and can only weigh 1 time. You label the the bottles 1, 2, 3, 4, 5. You may remove the pills from the bottle to weigh them. Find which bottle contains the 9mg pills. The weight from your one try is 147 mg.
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1 solution
Take 1 pill from bottle 1, 2 pills from bottle 2, 3 pills from bottle 3, 4 pills from bottle 4, and 5 pills from bottle 5. You should weigh 15 pills total. So here's how to get the answer. If Bottle number 1 had the 9mg pill the total weight would have been 149mg. If Bottle number 2 had the 9mg pill the total weight would have been 148mg. If Bottle number 3 had the 9mg pill the total weight would have been 147mg. If Bottle number 4 had the 9mg pill the total weight would have been 146mg. If Bottle number 5 had the 9mg pill the total weight would have been 145mg. Since Bottle 3 had the 9mg pills we got 147mg. That is because 12 of the pills weighed 10mg, and 3 weighed 9mg.