Question

Five men A, B, C, D or E are wearing caps of black and white colour without knowing the colour of their own caps. It is known that a man wearing a black cap always speaks the truth while one wearing a white cap always tells lies. If they make the following statements, find the colour worn by each of them.
A : I see black caps and one white cap
B : I see four white caps
C : I see one black and three white caps
D : I see four black caps
E : No statement

Answer 1

Hint: For solving this question you should know about the general mathematical concept of stack exchange. In this problem we will set the statements in expression form or denoting form. And then we will set the given data in a form to understand the real situation for every statement.

Complete step by step answer:
According to our question five men which are A, B, C, D and E are wearing caps of black colour and white colour. And they also don’t know about the colour of the cap which they are wearing.
And the conditions are given as that the man wearing black cap always speaks truth and the man wearing white cap always tells lie.
So, according to their statements if we set the data then

Situation	A	B	C	D	E
When A speaks		B	B	B	W
When B speaks	W		W	W	W
When C speaks	W	B		W	W
When D speaks	B	B	B		B

Now, let us consider the situation when B is telling the truth, then B has a black cap and rest all has a white cap
Now if Cs statement is true, But that would mean C has a balck cap which contradicts Bs statements. So B was lying.
But according to given question, D says he only sees one white cap, so he is lying as A is wearing a white cap as well.
Also, A says he sees only one white cap that means he is also lying.
Now the situation is whether C is saying truth or not.
If C is telling the truth then E is wearing black cap and so C is consistent.
But if C is lying then E is wearing a white cap and C has a white cap which makes B correct and it is impossible as we have determined it earlier.
So, the only possibility is C and E wearing Black caps and rest all wearing white caps.
Note: While solving these type of questions you have to be very much careful about the statements of the given questions. Because everything is depending upon that in this and if any statements is giving any wrong data with the statement then always find the real data with the statement then always find the real data present at there and then set the data again with the statement.