Coins Measuring Brain teaser
There are 6 coins, 4 of which are real and 2 are counterfeit. You are given a weighing balance and you are aware that the counterfeit coin is lighter.
What is the procedure to identify the 2 counterfeits?
Hint: Can be done in less than 3 weightings
Assuming that the balance is a common two-pan one (rather than a digital one), here’s a possible solution with MAX. 3 attempts:
Step 1: Split the coins into two sets of three coins each.
We have TWO possibilities: One, BOTH counterfeit coins are in the SAME set (Case 1) OR both sets contain one counterfeit each (Case 2).
Step 2: Weigh the sets against each other. (W1).
Case 1: The set containing the counterfeits will be lighter. In this case, take this set for the next step (to identify the counterfeits). Let the coins be C11, C12 and C13.
Step 3(1): Keep one coin (C11) aside. Now, since two of the three coins are counterfeits, we have two possibilities here. P1: Both the remaining coins (C12 AND C13) are counterfeit; P2: C11 and one of the other two coins (C12 OR C13) are counterfeit.
Step 4(1) W2: Weigh C12 and C13. If they are equal, both are counterfeit. Otherwise, the lighter of the two and C11 the counterfeits. SOLVED.
Case 2: Both the sets are of equal weight (because both contain one counterfeit each). Take any set. Let the coins be C21, C22, C23.
Step 3(2): Keep one coin (C21) aside. Again, we have two possibilities here: p1: the coin set aside (C21) is counterfeit; p2: One of the other two (C22 OR C23) is the counterfeit.
Step 4(2): W2: Weigh C22 and C23. If they are equal, both are good coins and C21 is the counterfeit. Otherwise, the lighter of the two (C22 / C23) is the counterfeit in the currently selected set. One of the counterfeits identified.
Step 5(2): W3: Repeat the Step 3(2) and 4(2) on the second set to determine the counterfeit in that set. BOTH Counterfeits identified; problem SOLVED.
More puzzles to try-
- A devotee goes to three temples, temple1, temple2 and temple3 one after the other. In front of each temple, there ...Read More »
- 3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »
- Five puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »
- In a country where everyone wants a boy, each family continues having babies till they have a boy. After some ...Read More »
- There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »
- Dr.Willam wants to operate for three different persons who were wounded. But he had only two surgical gloves. There is ...Read More »
- Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »
- In the gear arrangement, To which one will the needle touch, 1 OR 2Read More »
- Some numbers are very mysterious. They are all integers. They have more than one digit. If you multiply them with ...Read More »
- 100 persons are standing in line, each facing the same way. Each person is wearing a hat, either red or ...Read More »
- There is a perfectly accurate analog watch with hour, minute, and second hands. How many times a day do all three ...Read More »
- Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »
- Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »
- A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over ...Read More »
- In the middle of the confounded desert, there is the lost city of “Ash”. To reach it, you will have ...Read More »
- Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »
- A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »
- Jasmine, 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 markRead More »
- A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »