You have 5 jars of pills. Each pill weighs 10 gram, except
for contaminated pills contained in one jar, where each pill
weighs 9 gm. Given a scale, how could you tell which jar had
the contaminated pills in just one measurement?
Take 5 pills from jar 1, 4 pills from jar2,…. and 1 pill
from jar 5 and put altogether in the scale. the ideal
weight should be (1+2+3+4+5)x10= 150gms. for eg if the jar2
is contaminated then the weight will be 146 gms. so
depending on the amount of weight loss we can identify the
contaminated jar.
take 1,2,3,4&5 pills from jars 1,2,3,4&5 respectively.the
total weight of the contaminated pills should be a multiple
of 9 & that of normal pills shall be a multiple of 10.
so,if its jar 1 that is contaminated, the last digit of the
total weight of all the pills will be 9,if its jar2 that is
contaminated, then the last digit will be 8,if its jar3 it
will be 7,if its jar4 it will be 6 & if its jar5 it will be
5.
Take 5 pills from jar 1, 4 pills from jar2,…. and 1 pill
from jar 5 and put altogether in the scale. the ideal
weight should be (1+2+3+4+5)x10= 150gms. for eg if the jar2
is contaminated then the weight will be 146 gms. so
depending on the amount of weight loss we can identify the
contaminated jar.
take 1,2,3,4&5 pills from jars 1,2,3,4&5 respectively.the
total weight of the contaminated pills should be a multiple
of 9 & that of normal pills shall be a multiple of 10.
so,if its jar 1 that is contaminated, the last digit of the
total weight of all the pills will be 9,if its jar2 that is
contaminated, then the last digit will be 8,if its jar3 it
will be 7,if its jar4 it will be 6 & if its jar5 it will be
5.