I've chosen a two-digit positive integer n (i.e. 10 - 99) and tell its first digit to Ojas, its second digit to Paddy, and its digit sum to Quentin. The following conversation occurs, in which all three of them have perfect deduction skills, and "only now" means since the previous piece of knowledge:
Paddy: "The number isn't prime."
Ojas: "It isn't a perfect square."
Paddy: "I'm not sure if it is a triangle number or not."
Quentin: "I know what it is. But only now."
Ojas: "I only now know what it is."
What is n?
The required value of n is 45.
*** I will try to posit an independent analytic solution of my own.
Puzzle Answer
