**Question: **Professors Ahmad and Joshi are extremely strange persons.

Prof. Ahmad lies on Mondays, Tuesdays and Wednesdays, but tells true on other days of the week.

Prof. Joshi lies on Thursdays, Fridays and Saturdays, but tells true on other days of the week. **Case1: **They made the following statements:

Prof. Ahmad : "Yesterday was one of my lying days."

Prof. Joshi : "Yesterday was one of my lying days too."

What day of the week was it?

**Case2: ** Both Professors looked very alike and one day they said to a visitor to their

department :

First Prof: "I'm Ahmed."

Second Prof: "I'm Joshi."

Who was who? What day of the week was it?

**Case3:**On another occasion, both Professors made the following statements:

First Prof : 1. "I lie on Saturdays."

2. "I lie on Sundays."

Second Prof. : "I will lie tomorrow."

What day of the week was it?

**Answer:**

Mon Tue Wed Thu Fri Sat Sun

Prof. Ahmad Lies Lies Lies tells truth tells truth tells truth tells truth

Prof. Joshi tells truth tells truth tells truth Lies Lies Lies tells truth ** Case 1 : **

Assume that Prof. Ahmad is telling truth => today is Thursday

Assume that Prof. Ahmad is lying => today is Monday

Similarly, Assume Prof. Joshi is telling truth => today is Sunday

Assume that Prof. Joshi is lying => today is Thrusday.

Hence, today is Thrusday, Prof. Ahmad is telling truth and Prof. Joshi is lying.

**Case 2 :**

Assume that First Prof. is telling truth => Thursday, Friday, Saturday or Sunday

Assume that First Prof. is lying => Thursday, Friday or Saturday

Similarly, Assume Second Prof. is telling truth => Monday, Tuesday, Wednesday or Sunday

Assume that Second Prof. is lying => Monday, Tuesday, Wednesday

The only possibility is Sunday and both are telling truth.

**Case 3 :**

A simple one. First Prof. says - "I lie on Sunday" which is false as both the Prof. tell truth on sunday. It means the first statement made by the First Prof. is also false. It means the First Prof. tells truth on Saturday. Hence First Prof. is Prof. Ahmad and he is lying. It means that today is either Monday, Tuesday or Wednesday.

It is clear that Second Prof. is Prof. Joshi.

Assume that he is telling truth => today is Wednesday

Assume that he is lying => today is Saturday.

Hence, today is Wednesday !!!