Question

While Balbir had his back turned, a dog ran into his butcher shop, snatched a piece of meat off the counter and ran out. Balbir was mad when he realised what had happened. He asked three other shopkeepers, who had seen the dog, to describe it. The shopkeepers really did not want to help Balbir. So each of them made a statement which contained one truth and one lie.

• Shopkeeper number 1 said: "The dog had black hair and a long tail."
• Shopkeeper number 2 said: "The dog had a short tail and wore a collar."
• Shopkeeper number 3 said: "The dog had white hair and no collar."

Based on the above statements, which of the following could be a correct description?

• A. The dog had white hair, short tail and no collar
• B. The dog had black hair, long tail and no collar
• C. The dog had black hair, long tail and a collar
• D. The dog had white hair, long tail and a collar

Hint:

In each statement exactly one of the two parts is true. Test each option against all three statements.

Answer 1

The Correct Option is D

Step 1: Rule.
Each shopkeeper's statement has exactly one true part and one false part. A description is acceptable only if it makes exactly one part of every statement true.

Step 2: Test option (1): white, short tail, no collar.
Shopkeeper 1: black (false), long tail (false). Both parts false, so this is not allowed.

Step 3: Test option (4): white, long tail, collar.
Shopkeeper 1: black (false), long tail (true): one truth. Shopkeeper 2: short tail (false), collar (true): one truth. Shopkeeper 3: white (true), no collar (false): one truth. All three statements have exactly one truth, so this is allowed.

Step 4: Test options (3) and (2).
Both have black hair and a long tail, so Shopkeeper 1 would have both parts true. Not allowed.

Step 5: Note.
Enumerating all 8 combinations of hair, tail and collar, only 'white, long tail, collar' and 'black, short tail, no collar' work. The latter is not offered, so option (4) is the answer.

Final Answer:
The correct option is (4): The dog had white hair, long tail and a collar