Game for Four Students
By John P. Robertson

Four CAS students, Paula, Quentin, Richard, and Sally, will win a prize if each one succeeds at the following task. One by one they will be taken into a room where there are four curtains, numbered one to four. Four cards, each with one of the letters P, Q, R, and S, one card with each letter, are placed at random behind the curtains, one card behind each curtain. Each student will be allowed to look behind two curtains of their choosing. If they find a card with the first letter of their name behind one of the two curtains, they succeed. If all four students succeed, the group wins. If any student does not succeed, the group loses.

The students are allowed to agree on a strategy together before the first is taken into the room. However, once a student has been in the room, he or she cannot communicate with any student who has not been in the room. Additionally, students who have not been in the room have no way of knowing whether the students who have been in the room were successful or not.

If each student looks behind two curtains at random, each student has a probability of 50 percent of succeeding, and the group has a 6.25 percent probability of winning. Your challenge is to devise a strategy that would give the group a probability of over 40 percent of winning.

Double Crostic Solution

The solution to Alan K. Putney's marvelous double crostic is, "Misdirected goals, mistakenly measured by the amount of your compensation, the loftiness of your title, or the number of people reporting to you, should never be confused with success. Rather, the manner in which these things were attained and how they are put to use are much better indications of a productive life." This quote is from Albert Beer's "Address to New Members" in May 2003.

Marty Adler, Robert Ballmer, Rachel Berkowitz, John E. Captain, Frank Chang, Ann M. Conway, Todd Dashoff, John Herder, Charles C. Hewitt, Brian J. Mullen, David Rafferty, Deborah Rosenberg, Peter Royek, David L. Ruhm, Gregory Scruton, David Uhland, Melissa J. Vaughn, and Micah Woolstenhulme solved the double crostic.