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Logic Puzzles by The Logic Fiend
Good day my lamebrained friend. Be addled by my riddles. You may be rewarded or punished for your answers. So beware!

The challenge of the 9 eggs
Saturday, July 30, 2005
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 9 eggs -- 8 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 50 Protista Points! Winners:
- Wiggum1006
- le_battement
12 Comments.


Number the eggs 1-9. Weigh eggs 1,2,3 against 4,5,6. If the scale balances, then the odd egg must be one of 7,8, or 9. Weigh 7 and 8 against 5 and 6. If the scale balances again, #9 must be the odd egg. If the scale does not balance this second time, then weigh 7 and 9 against 5 and 6. If the scale balances, then #8 is the odd egg, and if it doesn't, then #7 is the odd egg. If the first measurement of 1,2,3 vs. 4,5,6 gives an imbalance, take note of which way it tips. Weigh 1 and 4 against 2 and 7. If it tips in the same direction, then #1 must be the odd egg. If it tips in the other direction, then #2 or 4 must be the odd egg and using the third use of the balance you can weigh #2 against 7. If the scale tips, then #2 is the odd egg, and if it doesn't, then #4 is the odd egg. If 1,4 vs. 2,7 doesn't tip the scale, then the odd egg must be 3,5, or 6. Weigh 5 and 7 against 6 and 8. If the scale tips in the same direction as the first weighing, then #6 must be the odd egg. If it tips in the other direction, then #5 must be the odd egg. If it doesn't tip at all, then #3 must be the odd egg.
» Wiggum1006 on 2005-08-02 11:16:21

I have one also
Wiggum, all due respect, but I wrote this at the same time as I saw yours come up, so rest assured that I was not plagiarizing you. I have not even read yours yet.

This is really conditional, but I may have happened upon a solution. Well, many, actually, since conditions change.

Solution #1
1. Weigh any 6 eggs, 3 to a side.
2. If they are even, add an egg to either side.
3. If they are even, the egg you have not weighed is the odd one.

Solution #2

1. Weigh any 6 eggs, 3 to a side.
2. If they are uneven, note the side that changed and remove one egg from either side.
3. If they are even, the egg you removed from the side that changed was the odd one.

Solution #3

1. Weigh any 6 eggs, 3 to a side.
2. If they are uneven, note the side that changed and remove one egg from either side.
3. If they are uneven still, remove another egg from either side.
4. If they are even, the egg you removed from the side that changed was the odd one.

Solution #4

1. Weigh any 6 eggs, 3 to a side.
2. If they are uneven, note the side that changed and remove one egg from either side.
3. If they are uneven still, remove another egg from either side.
4. If they are uneven still, the egg from the side that changed was the odd one.

» flanger001 on 2005-08-02 11:36:29

Wiggum is a winner!
I see you have returned to secure your status on the Hall of Fame.

re: Flanger
I believe you're missing a few scenarios, such as 2. even, 3. uneven. Also, how do you take a note of which side changed?
» theLogicFiend on 2005-08-03 09:14:39

whoops
That scenario is hard. Do none of the others work? They make sense to me.
» flanger001 on 2005-08-03 05:20:22

re: Flanger
Can you elaborate on how you determine which side is the one that "changed?"
» theLogicFiend on 2005-08-03 06:18:49

weigh two eggs at a time until they aren't perfectly balanced. Whichever one tips, baddabingbaddaboom.
» redintersectsme on 2005-08-03 10:50:37

even though i just thought that out and it totally wouldn't work. I still got to talk like an italian guy.
» redintersectsme on 2005-08-03 10:51:01

Label the 9 eggs A, B, C, D, E, F, G, H, I

1. Test ABC | DEF
If: The balance is even; G, H, or I is odd, then:
2. Test G | H
If: The balance is even; I is odd
If: The balance is off; then
3. Test G | I
If: The balance is even; H is odd
If: The balance is off; G is odd

1. Test ABC | DEF
If: The balance is off; A, B, C, D, E, or F is odd, then:
2. Test AD | BE
If: The balance is even; C or F is odd, then:
3. Test C | A
If: The balance is even; F is odd
If: The balance is off; C is odd

1. Test ABC | DEF
If: The balance is off; A, B, C, D, E, or F is odd, then:
2. Test AD | BE
If: The balance is off AND the heavy side from 1 is still heavy; A or E is odd, then:
3. Test A | F
If: The balance is even; E is odd
If: The balance is off; A is odd

1. Test ABC | DEF
If: The balance is off; A, B, C, D, E, or F is odd, then:
2. Test AD | BE
If: The balance is off AND the heavy side from 1 is no longer heavy; B or D is odd, then:
3. Test B | F
If: The balance is even; D is odd
If: The balance is off; B is odd
» le_battement on 2005-08-05 05:43:27

Le_battement is a winner!
Well done. Are there any more solutions?
» theLogicFiend on 2005-08-07 08:56:50

well obviously...
you watch the Uruguayan cockatoo on the nights of a full moon and mark the eggs that are laid... but if for some ingenius reason the powers of logic manage to get in your way ::shakes fist:: you might be able to lable your nine eggs 1, 2, 3, 4, 5, 6, 7, 8, and 9 then you put 1 to 2, 3 to 4, 5 to 6, 7 to 8, then you take which ever 2 eggs that are off balance and place both of them in seperate trials against eggs that balanced in the first step.
» monkeymeister on 2005-08-07 04:24:03

hey can i have my freakin pps now?
» monkeymeister on 2005-08-23 06:04:27

re: monkeymeister
Your logic escapes the logic fiend. Remember, you are only allowed to use the balance thrice.
» theLogicFiend on 2005-08-24 08:45:38

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