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.
Your Answer
More puzzles to try-
Microscopic Angle
How much will a 45° angle measure when looked at under a microscope that magnifies ten times?Read More »How many words
How many words can a pen with half refill write?Read More »Face and two hands but no arms or legs
What has a face and two hands but no arms or legs?Read More »Shoe Riddle
Who sleeps with their shoes on?Read More »Cricket Run Riddle
John has played 50 ODI’s and his average is 50. How many runs should he score in his 51st ODI, ...Read More »Can you crack the code to reveal a saying?
The Greek philosopher Pythagoras described three as the perfect number – it has a beginning, a middle and en end. ...Read More »Fireman, policeman and a doctor brain teaser
After looking for his long lost brother that he has never met before, Justin is able to find his brother’s ...Read More »ABCDE>>>>
What word or Phrase or letter is it representing abcdefghijklmnopqrstvwxyzRead More »Secret Message Riddle
Mr. Jacob is on a secret mission and it is 05 January so he wants to send a message to ...Read More »Specialized agency of the UN that deals with global health issues
Which organisation is a specialized agency of the UN that deals with global health issues? a) World Trade Organization (WTO) ...Read More »Spy under blanket
What do you call a spy who sleeps with a blanket over his head?Read More »Mission Impossible
What is both possible and impossible at the same time?Read More »Algebraic Rebus Puzzle
Can you decipher below algebraic riddle below?Read More »8 Question 1 Answer
What one word is- In ENGLISH name of a sweet? name of a medicine? name of a movie? Name of ...Read More »No.1 on chart riddle
On the charts I remain number one, This position cannot be undone, If I burn, you may get Just a ...Read More »Solve the Rebus meaning
Solve the rebus below.Read More »Complete the Sequence
2, 3, 5, 9, 17, _ What is the next number in the sequence?Read More »Divide in Equal Shape
Can you divide the below-given shape into four equal and identical pieces?Read More »How many do you have to draw to be sure that you have a pair?
There are 32 red socks and 32 blue socks in the drawer. You can’t tell which sock is right and ...Read More »Dress for everyone
What dress does everyone have, but no one wears?Read More »