# How Many Ways Can 8 Dice Be Arranged Using 4 Colors?

## School Name

James Island Charter High School

Mathematics

Mentored

## Abstract

How many ways can eight dice be arranged using four colors without counting inverses? An inverse is the flipping of the pattern so the color of dice one becomes the color for dice eight, the color of two becomes the color for seven, the color of three becomes the color of six, the color of four becomes the color for five, the color of five becomes the color for four, the color of six becomes the color for three, and the color for eight becomes the color for one. An example is G, Y, R, B, Y, B, G, R is the same as R, G, B, Y, B, R, Y, G. We first approached this question by breaking it down to four dice and four colors and drawing all possible arrangements. Once we had the number for this question, we were able to formulate an equation what would solve for eight dice and and four colors. This equation lead us to ask what would happen if there were n number of dice and four colors. Finally we created a true generalized equation by replacing the four colors with A colors.

RITA 273

## Start Date

3-23-2024 11:00 AM

Oral and Written

## Group Project

No

COinS

Mar 23rd, 11:00 AM

How Many Ways Can 8 Dice Be Arranged Using 4 Colors?

RITA 273

How many ways can eight dice be arranged using four colors without counting inverses? An inverse is the flipping of the pattern so the color of dice one becomes the color for dice eight, the color of two becomes the color for seven, the color of three becomes the color of six, the color of four becomes the color for five, the color of five becomes the color for four, the color of six becomes the color for three, and the color for eight becomes the color for one. An example is G, Y, R, B, Y, B, G, R is the same as R, G, B, Y, B, R, Y, G. We first approached this question by breaking it down to four dice and four colors and drawing all possible arrangements. Once we had the number for this question, we were able to formulate an equation what would solve for eight dice and and four colors. This equation lead us to ask what would happen if there were n number of dice and four colors. Finally we created a true generalized equation by replacing the four colors with A colors.