franKii924
The Riddle:You have twelve coins. You know that one is fake. The only thing that distinguishes the fake coin from the real coins is that its weight is imperceptibly different. You have a perfectly balanced scale. The scale only tells you which side weighs more than the other side.
What is the smallest number of times you must use the scale in order to always find the fake coin?Use only the twelve coins themselves and no others, no other weights, no cutting coins, no pencil marks on the scale. etc.
These are modern coins, so the fake coin is not necessarily lighter.
Presume the worst case scenario, and don't hope that you will pick the right coin on the first attempt.
**explain so i know its not a guess** Is it 5 tries? (I'm assuming that it's the worst case scenario with the least number of tries, right?)
Oh boy, this is going to be a LONG explanation.
- Split the 12 coins into 4 groups of 3 coins each.
- SCALE USE #1: Put one of the groups of 3 coins on each side of the scale (That means you're putting 3 coins on each side of the scale, 6 coins total on the scale at one time). In the worse scenario, each side will weigh the same and the fake coin is in one of the groups of 3 that has not been placed on the scale yet. Remove these coins from the scale and set them aside (separate from the other coins that have yet to be weighed); none of these coins are the fake one because these 2 groups of 3 coins each weighed the same.
- SCALE USE #2: Take one of the remaining groups of 3 coins. Put 2 of the 3 coins of that group on the scale (one on each side, 2 coins total on the scale at one time). In the worse case scenario, these coins will weigh the same, which means they are NOT the fake.
- SCALE USE #3: Take one of the coins that you just weighed off the scale (put it in the other pile that you set aside, since you know it's not the fake). Take the third coin of the group (you just weighed the other 2) and put it on the side of the scale that you just removed 1 coin from (remember which side) (you're weighing this coin that you just put on the scale against against a coin that you already know is not the fake). In the worse case scenario, these 2 coins will weigh the same, which means the new one (and the old one, but you already found that out) is NOT the fake coin. This means that one of the 3 coins in the last group (which you have not put on the scale yet) is the fake.
- SCALE USE#4: Take those coins that you just weighed off the scale an put it with those other NOT-fake coins. So, now we're down to 3 coins. Take 2 of these last 3 coins and put one on each side of the scale. In the worse case scenario, these 2 coins will NOT weigh the same. That means that 1 of the coins on the scale IS the fake (which means the third coin that hasn't been put on the scale yet is NOT fake).
- SCALE USE #5: Take one of the coins that is on the scale off the scale (this coin gets it's OWN pile, it might be the fake one) and put the last coin (that you have not put on the scale yet until now) on the side of the scale that is now empty (That means that you have one coin on each side of the scale again, one you just measured and the other one is now being weighed for the first time.
YOU HAVE TO REMEMBER WHICH ONE OF THE COINS ON EACH SIDE OF THE SCALE IS THE "OLD" ONE AND WHICH ONE IS THE "NEW" ONE!!!). If the 2 coins that are now on the scale weigh the same on the scale, then the coin that you put into it's own pile is the fake one. If the scale is uneven with the 2 coins that are now on it, then the "OLD" coin is the fake.
Ahh...finally. I'm done explaining. I really hope I'm right.
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