2022 MMATHS Individual Round Problems/Problem 4
Revision as of 12:29, 19 December 2022 by Arcticturn (talk | contribs) (Created page with "==Problem== Cat and Claire are having a conversation about Cat's favorite number. Cat says, "My favorite number is a two-digit perfect square!" Claire asks, "If I picked a di...")
Problem
Cat and Claire are having a conversation about Cat's favorite number. Cat says, "My favorite number is a two-digit perfect square!"
Claire asks, "If I picked a digit of your favorite number at random and revealed it to me without telling me which place it was in, is there a chance I'd know for certain what it is?"
Cat says, "Yes!" Moreover, if I told you a number and identified it as the sum of the digits of my favorite number, or if I told you a number and identified it as the positive difference of the digits of my favorite number, you wouldn't know my favorite number!
Claire says, "Now I know your favorite number!" What is Cat's favorite number?
