There are eight eggs which are identical in shape and look but one is lighter in weight. How is it possible for one to weigh only 2 times on a balance scale to find out the lighter egg?
Printable View
There are eight eggs which are identical in shape and look but one is lighter in weight. How is it possible for one to weigh only 2 times on a balance scale to find out the lighter egg?
Bob, Here is the solution.
Let us say we have eight eggs e1,e2,e3,e4,e5,e6,e7 and e8.
Group them as follows
Group G1 : e1,e2 and e3
Group G2 : e4,e5 and e6
Group G3 : e7 and e8
Put G1 at one end of balance scale and G2 at the other,
There are only two possible cases
Case 1: The balace scale is perfectly balanced.
then it must be either e7 or e8 which is lighter
now put e7 at one and and e8 at another end. Of course you can identify the lighter egg.
Case 2: Either group G1 or G2 lesser than the other one.
take the lesser Group now, let us say G1 is a lesser group.
now put e1 at one end and e2 at the other end.
if the balace scale is balaced perfectly then e3 is a lighter egg
else lesser among e1 or e2 is a lighter egg.
In both the cases we use the balace exactly twice.
I hope this helps you:)
-- James