2024 SSMO Relay Round 5 Problems

Problem 1

Let the super factorial be defined on positive integers as Find the largest positive integer such that that there are exactly positive integers such that has fewer than trailing zeroes.

Solution

Problem 2

Let In the game of high and low, the computer chooses two integers without replacement from the set . The computer displays the first integer and asks the player if the second integer is higher or lower. Given that the player always plays optimally, the chances of guessing correctly is for relatively prime positive integers and Find

Solution

Problem 3

Let Let be the maximum prime factor that divides How many values of satisfy both and

Solution