## 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.

12 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

Xmen says

May 11, 2018 @ 06:29

There is no one definite answer, it is a tree of decisions for the different outcomes and depending on the outcomes of each weighing you should not forget to take that into consideration when you do your next weighing. I will not write my solution but I will suggest a hint:- start with a group of 3 with 4 eggs in each group.

Good Luck

Deez nuts says

May 21, 2018 @ 14:23

Just put 6 on each side, that simple.

Dan says

May 22, 2018 @ 09:45

If the left side is heavier, which egg is the odd one out and is it heavier or lighter than the rest?

Laura says

August 12, 2018 @ 23:19

I wish I could attach a picture that would explain better than words, but I’ll try.

Begin by weighing eggs (1-4) vs. eggs (5-8).

Let’s begin with the first option in which this scale is equal. Its obviously eggs 9-12 then.

1a) You remove egg 12 and weigh eggs 9 & 10 vs. 11 & 1(or any constant) and the scale is equal. Its egg 12 and compare to any egg to determine if it’s heavier or lighter.

1b) You remove egg 12 and weigh eggs 9 & 10 vs. 11 and a constant and the scale tips left telling you 9 & 10 are heavier. Remove egg 10 and weigh eggs 9 & 11 vs. any two constants. If they’re equal, it’s egg 10 and it’s heavier (known from 1b). If the scale tips left again, it has to be egg 9 which is heavier. If it tips right, egg 11 is the lighter one.

Ok back to the beginning now and when we weigh eggs (1-4) vs. eggs (5-8) the scale tips left. Same scenario goes if it tips right, just opposite rules apply.

2a) Eggs 9-12 are ruled out and can act as constants. Remove eggs 3,4 & 8. Weigh 1,5,constant vs. 2,6,7 and the scale is even meaning you’re down to eggs that were removed. Set aside egg 3 and weigh 4,8 vs. any two constants. If it’s even it’s egg 3 and it’s heavier (known from first weigh-in). It it tips left again, it has to be egg 4 which is heavier. If it tips right, egg 8 is the lighter one out.

2b) Eggs 9-12 are ruled out and can act as constants. Remove eggs 3,4 & 8. Weigh 1,5,constant vs. 2,6,7 and the scale tilts left (ruling out 5,2 and the removed eggs) meaning 1 could be the heavier one or maybe 6 or 7 are lighter. Set aside 6 and weigh 1,7 vs two constants. If it’s even, it’s egg 6 and it’s lighter. If the scale tips left still, it’s egg 1 which is heavier. If it tilts right, it’s egg 7 which is lighter.

2c) Eggs 9-12 are ruled out and can act as constants. Remove eggs 3,4 & 8. Weigh 1,5,constant vs. 2,6,7 and the scale tilts right now. It’s either 5 or 2 as they were the only eggs that switched sides. Weigh egg 5 vs. any constant, if it’s even then it’s egg 2 which is heavier. If it’s not even then it’s quite certainly egg 5 which is the lighter one.

My brain hurts but how did I do??

Leave a comment