Consider the following information regarding a 3-digit PIN.
The correct PIN is
Step-by-Step Logic Solution:
1. Eliminate incorrect digits:
From Clue 2 [7 3 8], we know that "Nothing is correct." Therefore, the digits 7, 3, and 8 are not in the PIN.
2. Identify the first digit:
Look at Clue 5 [7 8 0]. Since 7 and 8 are eliminated, 0 must be a correct number. The clue says it is "wrongly placed" in the 3rd position. So, 0 must be in the 1st or 2nd position.
Now look at Clue 3 [9 0 6]. It says two numbers are correct but wrongly placed. We know 0 is one of them. Here, 0 is in the 2nd position and is "wrongly placed," which means 0 cannot be in the 2nd position. Combining this with the previous step, 0 must be in the 1st position.
3. Identify the third digit:
Look at Clue 1 [6 8 9]. We know 8 is not in the PIN. The clue says "One number is correct and correctly placed."
- If 6 were correct, it would be in the 1st position, but we already know 0 is in the 1st position.
- Therefore, 9 must be correct and correctly placed in the 3rd position.
4. Identify the middle digit:
From Step 2 and 3, we know 0 and 9 are the two correct numbers in Clue 3 [9 0 6]. This means 6 is not in the PIN.
Look at Clue 4 [6 1 5]. It says one number is correct but wrongly placed. Since 6 is out, either 1 or 5 is correct.
- If 1 were correct, it would be "wrongly placed" in the 2nd position, but that is the only spot left in our PIN [0 _ 9].
- Therefore, 5 must be the correct number. In Clue 4, it is in the 3rd position (wrongly placed), so it fits perfectly in the 2nd position.
Final Result:
The correct 3-digit PIN is 059.
Important Questions from Puzzle (Notes)
- Four individuals - P, Q, R and S - are suspects in a theft case. They make the following statements :
P says: "Q is guilty."
Q says: "R is guilty."
R says: "P is innocent."
S says: "I am innocent"
If it is known that exactly one of them is guilty, and only the guilty person lies (all innocent people tell the truth), then who is the guilty one? - There are five men - A, B, C, D and E, six women P, Q, R, S, T and Z. A, B, and R are advocates. S, Q, P, D and C are doctors and the rest are teachers. A team has to be selected from these eleven persons subject to the following conditions:
(I) A, P and Z have to be together.
(II) B cannot go with D or R.
(III) E and Q have to be together.
(IV) C and T have to be together.
(V) D and P cannot go together.
(VI) C cannot go with Q.
If the team formed consists of two male advocates, two lady doctors and one teacher, the members of the team can be: - Read the following informations and answer the question given below :
A total of nine cards consisting of four kings, four queens and one joker are distributed among three persons P, Q and R such as :
I. Q has two cards, P has three cards and R has four cards.
II. Person, who has maximum number of cards, does not have the joker.
III. Each one has atleast one king while Q has two kings.
Who has three queens ? - A boatman on a bank of a river has to carry a dog, a cat and a container full of milk to the other bank in a boat, one at a time. The cat cannot be left alone with the milk or with the dog on either bank. What is the minimum number of times the boatman has to cross the river to carry all to the other bank?
- How many minimum number of times water must be poured from a fully filled vessel of 12 litre capacity to an empty vessel of 8 litre capacity to transfer 6 litres of water while an empty vessel of 5 litre capacity is also available for use?
