1. A villager, while on the road, met Ihtar Pajo and Nasreddin Hodja. Here is their conversation:

Villager: - Good day.

Pajo and Nasreddin: - Good day.

Villager: - What day is it today?

Nasreddin: - Tomorrow I will speak the truth.

Villager: - Well, what day is it tomorrow?

Nasreddin: - Tomorrow is not Sunday.

The Villager turns to Pajo: - Pajo, at least you tell me what day it is today?

Pajo mumbles something and leaves.

The Villager turns to Nasreddin: - Now, I didn't hear that well. What did Pajo say?

Nasreddin: - He said it's not Monday.

Villager: - Well, now I know what day it is today. Goodbye.

Can you determine which day of the week the conversation took place, given that you know what the villager knows, which is that Pajo lies on Monday, Tuesday, and Wednesday, and speaks the truth on the other days, while Nasreddin lies on Thursday, Friday, and Saturday, and speaks the truth on the other days?
Solution. Given the conditions of the problem, Nasreddin's first statement cannot be made on Wednesday, because on Wednesday he speaks the truth, and the statement would be false, and he cannot make it on Saturday, because on Saturday he lies, and the statement would be true. In all other days, this statement is possible.

Nasreddin's second statement cannot be made on Thursday and Friday, because on those days he lies, and the statement would be true. In all other days, Nasreddin's statement is possible.

Thus, the conversation is taking place on Sunday, Monday, or Tuesday. In all these days, Nasreddin speaks the truth, so Pejo indeed said it was Monday.

However, Pejo would not say it was Monday on Sunday, because on Sunday he does not lie, and he would not say it was Monday on Monday, because then he would be lying.

Thus, the only remaining possibility is that the conversation is taking place on Tuesday. It is easily verified that on Tuesday neither of the given statements is impossible, so Tuesday is the required day.