ISI 2021

Question

Five men A, B, C, D, E are wearing caps of black or white color without each knowing the color of his cap. It is known that a man wearing a white cap will always speak the truth while a man wearing a black cap always lies. They make the following statements.:

 

A: I see three white and one black cap.

B: I see four black caps.

C: I see one white and three black caps.

D: I see four white caps.

 

Find the color of each person’s cap.

Answer 1

***please check if question is complete***

lets see from D’s perspective – he/she is seeing 4 White caps

→  so if D is saying truth then A, B, C, E are wearing White caps and are saying truth but still B, C are seeing more than 1 Black caps.

→ so D must be lying → thus we can confirm D is wearing Black Cap

 

lets see from B’s perspective – he/she is seeing 4 Black caps

→ so if B is saying truth then A, C, D, E are wearing Black caps and B is wearing White cap.

→ but C is saying he’s seeing 1 White cap (B) and 3 Black caps (A, D, E) which is true according to B. So, C is saying truth even when wearing Black cap. This is contradiction so we can confirm B is wearing Black Cap

 

lets see from A’s perspective – he/she is seeing 3 White and 1 Black cap.

→ but we already know B and D are wearing Black caps → so A is lying and we can confirm A is wearing Black Cap 

 

lets see from C’s perspective – he/she is seeing 1 White and 3 Black cap.

→ suppose C is saying truth then those 3 Black caps are A, B, D and white cap must be E

→ we can not prove that C is lying so we’ll consider he/she is saying truth and C is wearing White cap

 

White caps – C and E

Black Caps – A, B and D