Are Stupid Dice Necessary?

Summary

A pair of 6-sided dice cannot be relabeled to make the sums 2, 3, … 12 equally likely. It is possible to label seven, 10-sided dice so that the sums 7, 8, …, 70 occur equally often. We investigate such relabelings for pq-sided dice, where p and q are distinct primes, and show that these relabelings usually involve stupid dice, that is, dice with the same label on every face.

Additional information

Notes on contributors

Frank Bermudez

Frank Bermudez ([email protected]) received a B.S. and M.S. from Cal Poly Pomona. He is currently an adjunct mathematics professor at Chaffey College and Pasadena City College. Outside the classroom, Frank enjoys hiking and playing the drums.

Anthony Medina

Anthony Medina ([email protected]) is a graduate student at Cal Poly Pomona who plans to teach mathematics one day to young, eager minds. When not doing math, he will be found playing his guitar, reading comic books, or snuggling with his dogs. (He's not a geek at all.)

Amber Rosin

Amber Rosin ([email protected]) received a B.A. from Brown and an M.A. and Ph.D. from the University of California at Santa Barbara. She is an associate professor at Cal Poly Pomona, where she has absolutely amazing students. Apart from mathematics, she enjoys reading fiction, spending time with her husband, and dressing their cats in costumes.

Eren Scott

Eren Scott ([email protected]) is working on an M.S. in pure mathematics at Cal Poly Pomona, where he also received a B.S. After graduation, he plans to attend law school. Outside of school, he enjoys swing dancing and devising tortuous puns.