Well, well, well... your brains have fermented long enough! It is time for round two of the challenge of the eggs! MuHaHAHAHAa!!!

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To the logic fiend, it's a widely known fact that the South Uruguayan cockatoo only lays eggs that are 12 oz. Well, actually there is an exception. If a cockatoo lays an egg on the night of a full moon, the egg will deviate slightly from the 12 oz. norm.

A logic fiend gives you 12 eggs -- 11 are 12 oz., but 1 is not. The logic fiends also gives you a very accurate balance and tells you to determine the odd egg out with only 3 uses of the balance. Here is a picture of the balance.



How do you do it?

Each unique solution will earn you 100 pps.

Categories: brain teaser [t], logic puzzle [t]

Begin by weighing
1. ABCD| EFGH
If balanced, I, J K, L must be odd.
Weigh
2. AB | IJ
If balanced, K,L must be odd.
Weigh
3. A | K. If balanced, L must be odd. If not balanced, K is odd.

1. ABCD| EFGH
If balanced, I, J K, L must be odd.
Weigh
2. AB | IJ
If not balanced, I,J must be odd.
Weigh
3. A | I. If balanced, J must be odd. If not balanced, I is odd.

1. ABCD|EFGH
If unbalanced, A, B, C, D, E, F, G, or H must be odd. Note heavy side.
2. Weigh ABE | CDF.
If balanced, G,H must be odd.
3. Weigh G | L. If balanced, H is odd. If not balanced, G is odd.

1. ABCD| EFGH
If unbalanced, A, B, C, D, E, F, G, or H must be odd. Note heavy side.
2. Weigh ABE | CDF.
If unbalanced, A, B, C, D, E, or F must be odd. If heavy side has not changed, A, B, F are odd.
3. Weigh B | A. If balanced, F is odd. If unbalanced with heavy side unchanged, B is odd. If unbalanced with heavy side changed, A is odd.

1. ABCD| EFGH
If unbalanced, A, B, C, D, E, F, G, or H must be odd. Note heavy side.
2. Weigh ABE | CDF.
If unbalanced, A, B, C, D, E, or F must be odd. If heavy side has changed, C, D, E are odd.
3. Weigh C | D. If balanced, E is odd. If unbalanced with heavy side unchanged, D is odd. If unbalanced with heavy side changed, C is odd.

» Zanzibar on 2007-01-07 01:25:26

Weighing #1: ABCD vs. EFGH

    Outcome #1A: If ABCD = EFGH, then IJKL has the odd egg
    Weighing #2: IJK vs. ABC
        Outcome #1A.2A: If IJK = ABC, then L is odd
        Weighing #3: L vs. any other egg
            Outcome #1A.2A.3A: If L > other egg, then L is heavier than 12 oz.
            Outcome #1A.2A.3B: If L < other egg, then L is lighter than 12 oz.
        Outcome #1A.2B: If IJK > ABC, then IJK has a heavy (>12 oz.) egg
        Weighing #3: I vs. J
            Outcome #1A.2B.3A: If I = J, then K is the heavy egg
            Outcome #1A.2B.3B: If I > J, then I is the heavy egg
            Outcome #1A.2B.3C: If I < J, then J is the heavy egg
        Outcome #1A.2C: If IJK < ABC, then IJK has a light ( J, then J is the light egg
            Outcome #1A.2C.3C: If I < J, then I is the light egg

    Outcome #1B: If ABCD > EFGH, then either ABCD contains a heavy egg or EFGH contains a light egg
    Weighing #2: ABE vs. CFI
        Outcome #1B.2A: If ABE = CFI, then either D is the heavy egg or G or H is the light egg
        Weighing #3: G vs. H
            Outcome #1B.2A.3A: If G = H, so D is the heavy egg
            Outcome #1B.2A.3B: If G > H, then H is the light egg
            Outcome #1B.2A.3C: If G < H, then G is the light egg
        Outcome #1B.2B: If ABE > CFI, then either F is the light egg, or A or B is the heavy egg
        Weighing #3: A vs. B
            Outcome #1B.2B.3A: If A = B, then F is the light egg
            Outcome #1B.2B.3B: If A > B, then A is the heavy egg
            Outcome #1B.2B.3C: If A < B, then B is the heavy egg
        Outcome #1B.2C: If ABE < CFI, then either C is the heavy egg, or E is the light egg
        Weighing #3: C vs. any other egg except E
            Outcome #1B.2C.3A: If C = non-E egg, then E is the light egg
            Outcome #1B.2C.3B: If C > non-E egg, then C is the heavy egg

    Outcome #1C: If ABCD < EFGH, then either ABCD contains a light egg or EFGH contains a heavy egg
    Weighing #2: AEF vs. BGI
        Outcome #1C.2A: If AEF = BGI, then either H is the heavy egg or C or D is the light egg
        Weighing #3: C vs. D
            Outcome #1C.2A.3A: If C = D, then H is the heavy egg
            Outcome #1C.2A.3B: If C > D, then D is the light egg
            Outcome #1C.2A.3C: If C < D, then C is the light egg
        Outcome #1C.2B: If AEF > BGI, then either E or F is the heavy egg or B is the light egg
        Weighing #3: E vs. F
            Outcome #1C.2B.3A: If E = F, then B is the light egg
            Outcome #1C.2B.3B: If E > F, then E is the heavy egg
            Outcome #1C.2B.3C: If E < F, then F is the heavy egg
        Outcome #1C.2C: If AEF < BGI, then either G is the heavy egg or A is the light egg
        Weighing #3: A vs. any other egg except G
            Outcome #1C.2C.3A: If A = non-G egg, then G is the heavy egg
            Outcome #1C.2C.3B: If A < non-G egg, then A is the light egg
» ranor on 2007-01-07 02:02:50

Am I oversimplifying this?
You might hate me because I don't use variables to explain my answer, but here goes:

1. I would divide the eggs & weigh 6 on each side, Of course since one is odd, the scale would tip to show which side was lighter. I would then take the group of lighter eggs & put away the other side.

2. I would then divide the eggs 3 on each side. Again, I'd keep the lighter side & discard the rest.

3. Now comes the part that maybe I'm oversimplifying. I have three eggs left, so I'd take any 2 out of the 3 to find the odd one out. How would I do it? Simple:

a) If the eggs are even, it means the one I didn't weigh is the odd one out.
b) If the eggs are not even, the lighter one must be the odd one out!

I must be oversimplifying this.. It's probably not as easy as I'm thinking it is. =(
» rowenabautista on 2007-10-13 07:10:27

Your solution works if you know with certainty that the odd egg out is either heavier or lighter. The problem with this question is that we know that one is not 12 oz., but we have no indication in the text of the problem whether the odd egg it is heavier or lighter than 12 oz. That's why I did my solution the way that I did: using the method I outlined will tell you which egg is the odd one out, AND whether it is heavier or lighter than the others.
» ranor on 2007-10-14 11:57:24

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