top button
Flag Notify
    Connect to us
      Site Registration

Site Registration

Assuming that Neel and Nitin are perfectly logical and are always telling the truth, what was the original number?

+1 vote
131 views

I have chosen a positive integer between 5 and 15 inclusive.

I gave Neel the number of positive divisors of this number and Nitin the sum of positive divisors of this number.

Then the following conversation takes place:

Neel: "I don't know the original number."
Nitin: "I don't know the original number either."
Neel: "Now I know the original number."
Nitin: "Me too!"

Assuming that they both are perfectly logical and are always telling the truth, what was the original number?

posted Jul 20, 2018 by anonymous

Share this puzzle
Facebook Share Button Twitter Share Button LinkedIn Share Button

1 Answer

+1 vote

11 was the original number


lets look at the numbers first, see this table:


enter image description here


Neel: "I don't know the original number." - number of divisors are either 2 or 4, odd numbers (3 & 6) now excluded as Neel doesn't know the number, numbers 2&4 repeated in last raw of the table and he can't see which one is correct,
Nitin: "I don't know the original number either." - sum of divisors are either 12 or 24, odd numbers (6,8,14,15,18) excluded as Nitin doesn't know the number, numbers 12&24 repeated in the 3rd raw of the table and he can't see which one is correct,
We have now 4 numbers left- 6 (12/4), 11 (12/2), 14 (24/4) and 15 (24/4)
Neel: "Now I know the original number." - odd number is left among 4 numbers, which is number 2, the original number is 11
Nitin: "Me too!"- same logic, understands that it is number 11

answer Jul 21, 2018 by Hanifa Mammadov



Similar Puzzles
+2 votes

Statement: I am lying and I always lies.

Tell me whether I am lying or telling the truth?

0 votes

Suppose you are visiting an island with knights who always tell the truth, knaves who always lie, and jokers who can do either.

You meet three islanders named Ellis, Farin and Gobi. They make the following statements:

Ellis says, "Farin is a joker."
Farin says, "Gobi is a joker."
Gobi says, "Ellis is a joker."

If you know exactly one of them is a joker, how many of them are knights?

+1 vote

Abby, Bobby, Clyde, David, and Evangeline are causing trouble by confusing people with weird statements, and you have to break all their shenanigans. You make an ultimatum: if you solve a riddle of their creation, they have to stop causing trouble. The five agree to your conditions and start making statements:

Abby: I am telling the truth
Bobby: Clyde or Abby is lying but not both.
Clyde: I am telling the truth.
David: Bobby is telling the truth.
Evangeline: Clyde is telling the truth.

Given that there is only one answer, all people in the answer choices have made a statement, and statements must be true or false but not both, which person is telling the truth?

...