Problem Of the Week: 11th March 2024

There are 25 red balls and 25 blue balls in a bag. Alice and Bob take turns drawing balls from the bag without replacement, with Alice going first. Interestingly, they notice that whenever a red ball was drawn, the next ball drawn (by any person) was never red. Suppose Bob drew m red balls. Given that the 33rd ball drawn was red, what is the sum of all possible values of m?