WHICH IS THE FAKE COIN
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.
If you knew the fake coin was lighter, then the solution would have an easy explanation. But you do not. So….
Number the coins 1 through 12.
1. Weigh coins 1,2,3,4 against coins 5,6,7,8.
1.1. If they balance, then weigh coins 9 and 10 against coins 11 and 8 (we know from the first weighing that 8 is a good coin).
1.1.1. If the second weighing also balances, we know coin 12 (the only one not yet weighed) is the counterfeit. The third weighing indicates whether it is heavy or light.
1.1.2. If (at the second weighing) coins 11 and 8 are heavier than coins 9 and 10, either 11 is heavy or 9 is light or 10 is light. Weigh 9 against 10. If they balance, 11 is heavy. If they don’t balance, you know that either 9 or 10 is light, so the top coin is the fake.
1.1.3 If (at the second weighing) coins 11 and 8 are lighter than coins 9 and 10, either 11 is light or 9 is heavy or 10 is heavy. Weigh 9 against 10. If they balance, 11 is light. If they don’t balance, you know that either 9 or 10 is heavy, so the bottom coin is the fake.
1.2. Now if (at first weighing) the side with coins 5,6,7,8 are heavier than the side with coins 1,2,3,4. This means that either 1,2,3,4 is light or 5,6,7,8 is heavy. Weigh 1,2, and 5 against 3,6, and 9.
1.2.1. If (when we weigh 1,2, and 5 against 3,6 and 9) they balance, it means that either 7 or 8 is heavy or 4 is light. By weighing 7 and 8 we obtain the answer, because if they balance, then 4 has to be light. If 7 and 8 do not balance, then the heavier coin is the counterfeit.
1.2.2. If (when we weigh 1,2, and 5 against 3,6 and 9) the right side is heavier, then either 6 is heavy or 1 is light or 2 is light. By weighing 1 against 2 the solution is obtained.
1.2.3. If (when we weigh 1,2, and 5 against 3, 6 and 9) the right side is lighter, then either 3 is light or 5 is heavy. By weighing 3 against a good coin the solution is easily arrived at.
1.3 If (at the first weighing) coins 1,2,3,4 are heavier than coins 5,6,7,8 then repeat the previous steps 1.2 through 1.2.3 but switch the numbers of coins 1,2,3,4 with 5,6,7,8.
More puzzles to try-
What is the logic behind these ?3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »
Defective stack of coins puzzleThere are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »
Which clock works best?Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »
(Advanced) Cheryl’s Birthday PuzzlePaul, Sam and Dean are assigned the task of figuring out two numbers. They get the following information: Both numbers ...Read More »
Five greedy pirates and gold coin distribution PuzzleFive puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »
Magical flowers!!A devotee goes to three temples, temple1, temple2 and temple3 one after the other. In front of each temple, there ...Read More »
Tuesday, Thursday what are other two days staring with T?Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »
How could only 3 apples leftTwo fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »
How Many Eggs ?A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over ...Read More »
HARD MATHS – How much faster is one train from other PuzzleTwo trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination ...Read More »
Most Analytical GOOGLE INTERVIEW Question RevealedLet it be simple and as direct as possible. Interviewer : Tell me how much time (in days) and money would ...Read More »
Lateral thinking sequence PuzzleSolve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »
How did he know?A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »
Pizza Cost Math Brain TeaserJasmine, Thibault, and Noah were having a night out and decided to order a pizza for $10. It turned out ...Read More »
Which letter replaces the question markWhich letter replaces the question markRead More »
Which room is safest puzzleA murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »
Richie’s Number SystemRichie established a very strange number system. According to her claim for different combination of 0 and 2 you will ...Read More »
Srabon wanted to passThe result of math class test came out. Fariha’s mark was an even number. Srabon got a prime!! Nabila got ...Read More »
Become Normal!!Robi is a very serious student. On the first day of this year his seriousness for study was 1 hour. ...Read More »
Sakib Knows The Number!Ragib: I got digits of a 2 digit number Sakib: Is it an odd? Ragib: Yes. Moreover, the sum of ...Read More »