On Sunday, Oct. 27, 2019, three teams of three students each—one from Yeshiva College and two from Stern College for Women—traveled to the New Jersey Institute of Technology in Newark, New Jersey, to take part in a five-hour contest, competing against such universities as Columbia, Princeton, Rutgers and Cornell.

Dr. Joshua Waxman, assistant professor of computer science at Stern College for Women, was their coach.

Contestants were given 11 problems and needed to write computer programs in a programming language of their choosing to solve as many problems as possible in as short a time as possible. (Stern College used Python 3; Yeshiva College, Java.)

Here are two samples of the problems the teams faced:

**Sample 1**

In the *Pass the Buck* game, there are several players and each player has one or more neighbors among the other players. Each game begins with one player chosen at random who receives a buck (the current holder). (For this game, chosen at random means each possible outcome has the same probability.) Then, at each step, if the current holder has * d* neighbors, he/she chooses an integer

*in the range [*

**k***] at random. If*

**0, d***is chosen, the current holder is the winner and keeps the buck. Otherwise, the holder passes the buck to the neighbor with index*

**0***, who becomes the new holder. The game continues until some holder wins. Write a program to find the probability that player*

**k***wins if player*

**j***is the first holder.*

**k****Sample 2**

On February 15, 2012, the *New York Times* reported a flaw in the method of generating keys for a public-key encryption system. This flaw enables an attacker to determine private keys given a set of flawed public keys. Your job is to write a program that takes flawed public keys and determines the corresponding private keys.

For the purposes of this problem, a private key consists of a pair of prime numbers

2 < K_{1}, K_{2} < 2^{31}

and the corresponding public key consists of the product K_{1} x K_{2}

While they did not dominate the competition (Cornell ended up winning), the three teams were among the many teams that finished about one-third of the problems, testifying to their difficulty and the pressure of the situation.

Onward to next year’s contest!