## Balance Twelve Eggs

Suppose you have twelve eggs and a balance scale. All of the eggs are identical except for one whose only difference is its weight. Using the scale only three times, determine which egg is the odd egg out and whether it is heavier or lighter than the other eggs.

Weigh four against four. If they’re equal, weigh three of them against three you haven’t weighed. If they balance too, weigh the last remaining egg against any of the others to see if it is lighter or heavier. If the three suspects are heavier, weigh one of them against another and the one that goes down is it. If they balance the remaining suspect is heavy. Use the same process if they’re lighter. If the initial four vs four don’t balance, weigh two heavy eggs and a light egg against one heavy egg, one light one and a known normal egg. If they balance weigh the remaining two light eggs against each other. If they balance the unweighed heavy egg is the odd one out. If the side with two heavy eggs goes down weigh them against each other. If they balance it is the light egg on the other side. If the other side goes down it is either because of one heavy egg on that side or because the one light egg on the other side is lighter than the rest. Weigh one of them against a known normal egg to determine which is true.

8 Comments on "Balance Twelve Eggs"Orla says

December 28, 2015 @ 11:30

This seems unduly complicated. Weigh 4 against 4. Whichever group of 4 is heavier, weigh 2 against 2 within that group. Then weigh 1 against 1 within the heavier group of two. You can start with 2 groups of 5 eggs also.

Gabby says

June 4, 2016 @ 23:08

Tried it and got scrambled eggs.

kay says

August 21, 2016 @ 18:03

Lol @Gabby… that’s the best answer

Dan says

August 22, 2016 @ 20:11

@Orla You didn’t explain what to do if the first two groups are the same weight.

Me says

December 18, 2016 @ 13:36

This problem is overhard

(Thanks, Gabby) It scrambles your mind as your blood boils

It releases your inner devil as the weight of it all falls on your shoulders

Jason says

January 15, 2017 @ 17:35

Orla. Awesome answer if we knew whether the odd egg is heavier or lighter but since we don’t know 4 on 4 then 2 on 2 and then 1 on 1 doesn’t really work since you will not know which 4 to chose if they are not of equal weight. Is it lighter or heavier?

Lisa says

March 29, 2017 @ 11:13

This is hard I tried it for my class and no one got it

Here says

February 7, 2018 @ 17:35

Weigh four against four. If they’re equal, weigh three of them against three you haven’t weighed. If they balance too, weigh the last remaining egg against any of the others to see if it is lighter or heavier. If the three suspects are heavier, weigh one of them against another and the one that goes down is it. If they balance the remaining suspect is heavy. Use the same process if they’re lighter. If the initial four vs four don’t balance, weigh two heavy eggs and a light egg against one heavy egg, one light one and a known normal egg. If they balance weigh the remaining two light eggs against each other. If they balance the unweighed heavy egg is the odd one out. If the side with two heavy eggs goes down weigh them against each other. If they balance it is the light egg on the other side. If the other side goes down it is either because of one heavy egg on that side or because the one light egg on the other side is lighter than the rest. Weigh one of them against a known normal egg to determine which is true right

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