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- #51
Don't mean to sound smug or anything, but this one is pretty easy to get when you think about it.
Game Post your Puzzles / Brain Teasers
- Thread starter RobbieGray17
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Ok let me have a go.
In the solution below, I include the bracketed comments (assume left) and (assume right) to describe a scale that is heavier on the left than the right. If it is the other way around (right heavier than left), it doesn't matter. Walk around to the other side of the table to view it as stated if it makes you feel better) 
WEIGH #1: Put 4 coins on left scale, 4 on right scale and 4 in your pocket.
If the scales (WEIGH #1) are even:
- then you know all 8 of those coins are good. Mark one of them "GOOD" for reference, and put all 8 coins on the floor out of the way.
- WEIGH #2 : take 2 coins out of your pocket (leaving 2 in your pocket), and put 1 on each scale.
If the scales (WEIGH #2) are even:
- then you know these are good, and one of the two remaining in your pocket is fake.
- WEIGH #3: put 1 of these from your pocket on the left scale, and the marked "GOOD" one (from the floor!) on the right scale.
- If the scales are uneven, the coin on the left scale is fake. If they are even, the one in your pocket is fake.
If the scales (WEIGH #2) are uneven:
-then you know one of these is fake, but which one?
- WEIGH #3: replace the coin on the left scale with the coin marked "GOOD", keeping the original coin from that scale in your left hand.
- If the scales are even, the coin in your left hand is fake. If they are uneven, the one on the right scale is fake.
If the scales (WEIGH #1) are uneven:
- then you know the 4 in your pocket are good. Mark all of them "GOOD" for reference, and put all 4 coins on the floor out of the way.
- mark the four coins on the "heavier" scale with "PH" (potentially heavy).
- mark the four coins on the "lighter" scale with "PL" (potentially light).
- REMEMBER, a coin marked "potentially heavy" can be actually "GOOD" or actually "HEAVY", but NEVER "LIGHT"
- Likewise, a coin marked "potentially light" can be actually "GOOD" or actually "LIGHT", but NEVER "HEAVY"
- you should now have these coins:
Heavier (assume left) scale: [ PH, PH, PH, PH ] Lighter (assume right) scale: [ PL, PL, PL, PL]
WEIGH #2: Replace three of the PH coins with GOOD. Replace three of the PL coins with PH. You will have: Left scale: [ PH, GOOD, GOOD, GOOD ] Right scale: [PL, PH, PH,PH]
If the scales stay imbalanced the same way, left heavy (WEIGH #2):
Either the left PH or the right PL are fake. Name them PH2 and PL2
WEIGH #3: Weigh PH2 against a single GOOD coin. If PH2 is heavier, it is a heavy FAKE. If the scales balance, PL2 is a light FAKE.
If the scales tip to be imbalanced in the other direction, right heavy (WEIGH #2):
One of the three PH on the right must be a heavy fake. Label them PH1, PH2, PH3
WEIGH #3: Weigh PH1 against PH2. If there is a heavier one, it is the heavy FAKE. If they balance, PH3 is the heavy FAKE.
If the scales become balanced (WEIGH #2):
All these coins must be good, and thus on of three PLs you discarded before weigh #2 must be a light fake. Name them PLD1, PLD2, PLD3
WEIGH #3: Weigh PLD1 against PLD2. If there is a lighter one, it is the light FAKE. If they balance, PLD3 is the light FAKE.
That took a while, especially the "initial unbalanced" scenario. I think the tricky part is that at some point you have one weigh and three candidates - its important to eliminate one possibility (light or heavy) for those three and group them accordingly.
WEIGH #1: Put 4 coins on left scale, 4 on right scale and 4 in your pocket.
If the scales (WEIGH #1) are even:
- then you know all 8 of those coins are good. Mark one of them "GOOD" for reference, and put all 8 coins on the floor out of the way.
- WEIGH #2 : take 2 coins out of your pocket (leaving 2 in your pocket), and put 1 on each scale.
If the scales (WEIGH #2) are even:
- then you know these are good, and one of the two remaining in your pocket is fake.
- WEIGH #3: put 1 of these from your pocket on the left scale, and the marked "GOOD" one (from the floor!) on the right scale.
- If the scales are uneven, the coin on the left scale is fake. If they are even, the one in your pocket is fake.
If the scales (WEIGH #2) are uneven:
-then you know one of these is fake, but which one?
- WEIGH #3: replace the coin on the left scale with the coin marked "GOOD", keeping the original coin from that scale in your left hand.
- If the scales are even, the coin in your left hand is fake. If they are uneven, the one on the right scale is fake.
If the scales (WEIGH #1) are uneven:
- then you know the 4 in your pocket are good. Mark all of them "GOOD" for reference, and put all 4 coins on the floor out of the way.
- mark the four coins on the "heavier" scale with "PH" (potentially heavy).
- mark the four coins on the "lighter" scale with "PL" (potentially light).
- REMEMBER, a coin marked "potentially heavy" can be actually "GOOD" or actually "HEAVY", but NEVER "LIGHT"
- Likewise, a coin marked "potentially light" can be actually "GOOD" or actually "LIGHT", but NEVER "HEAVY"
- you should now have these coins:
Heavier (assume left) scale: [ PH, PH, PH, PH ] Lighter (assume right) scale: [ PL, PL, PL, PL]
WEIGH #2: Replace three of the PH coins with GOOD. Replace three of the PL coins with PH. You will have: Left scale: [ PH, GOOD, GOOD, GOOD ] Right scale: [PL, PH, PH,PH]
If the scales stay imbalanced the same way, left heavy (WEIGH #2):
Either the left PH or the right PL are fake. Name them PH2 and PL2
WEIGH #3: Weigh PH2 against a single GOOD coin. If PH2 is heavier, it is a heavy FAKE. If the scales balance, PL2 is a light FAKE.
If the scales tip to be imbalanced in the other direction, right heavy (WEIGH #2):
One of the three PH on the right must be a heavy fake. Label them PH1, PH2, PH3
WEIGH #3: Weigh PH1 against PH2. If there is a heavier one, it is the heavy FAKE. If they balance, PH3 is the heavy FAKE.
If the scales become balanced (WEIGH #2):
All these coins must be good, and thus on of three PLs you discarded before weigh #2 must be a light fake. Name them PLD1, PLD2, PLD3
WEIGH #3: Weigh PLD1 against PLD2. If there is a lighter one, it is the light FAKE. If they balance, PLD3 is the light FAKE.
That took a while, especially the "initial unbalanced" scenario. I think the tricky part is that at some point you have one weigh and three candidates - its important to eliminate one possibility (light or heavy) for those three and group them accordingly.
