question
You are given 10 jars of pills. One jar is filled with contaminated pills. Regular
and contaminated pills are identical - only to be differentiated by their weight.
Regular pills weigh 10 grams while contaminated ones weigh 1.1 grams. You
are provided a scale and allowed only one measurement. How do you identify which jar is contaminated?
Think of how to combine the weights of pills from all jars into one weight.
1) Take 1 pill from jar 1, 2 pills from jar 2, 3 pills from jar 3, and so on...
2) Weigh the pills taken from all the jars.
3) If jar 1 was contaminated then total weight would be: 1.1g + 540g (summation of weight of pills taken from jars 2 through 10) = 541.1g
If jar 2 was contaminated: 10g (one pill from jar 1) + 2.2g (weight of two contaminated pills from jar 2) + 520g (summation from 3 to 10) = 532.2g
Essentially the tenths place digit will give you the contaminated jar number with the exception if jar 10 is contaminated. Jar 10 will have a weight with tenths place equal to 0 (1.1g * 10 = 11.0g).
2) Weigh the pills taken from all the jars.
3) If jar 1 was contaminated then total weight would be: 1.1g + 540g (summation of weight of pills taken from jars 2 through 10) = 541.1g
If jar 2 was contaminated: 10g (one pill from jar 1) + 2.2g (weight of two contaminated pills from jar 2) + 520g (summation from 3 to 10) = 532.2g
Essentially the tenths place digit will give you the contaminated jar number with the exception if jar 10 is contaminated. Jar 10 will have a weight with tenths place equal to 0 (1.1g * 10 = 11.0g).