Confucius appears in Problem 1. A board holds 2,026 integers, each greater than 1, and the philosopher keeps picking two of them and replacing the pair with their greatest common divisor and a second value built from their least common multiple.
He repeats this for as long as he can. Contestants had to prove the process always ends with exactly one number left above 1, and that the number is the same no matter which pairs he chose along the way.
Liu Bang and Xiang Yu share Problem 3. The two warlords fought a civil war for control of China after the Qin dynasty collapsed, and the winner founded the Han.
Here they have a stick of length 1 and want to split it. Each marks up to n points on it, the stick is cut at every mark, and the two take turns claiming pieces with Liu Bang going first.
Contestants had to work out, for every n, the largest total length Liu Bang can guarantee himself whatever his rival does.
