Difference between revisions of "2023 IOQM/Problem 7"
(Created page with "==Problem 7== Unconventional dice are to be designed such that the six faces are marked with numbers from <math>1</math> to <math>6</math> with <math>1</math> and <math>2</mat...") |
(→Solution) |
||
| Line 2: | Line 2: | ||
Unconventional dice are to be designed such that the six faces are marked with numbers from <math>1</math> to <math>6</math> with <math>1</math> and <math>2</math> appearing on opposite faces. Further, each face is colored either red or yellow with opposite faces always of the same color. Two dice are considered to have the same design if one of them can be rotated to obtain a dice that has the same numbers and colors on the corresponding faces as the other one. Find the number of distinct dice that can be designed. | Unconventional dice are to be designed such that the six faces are marked with numbers from <math>1</math> to <math>6</math> with <math>1</math> and <math>2</math> appearing on opposite faces. Further, each face is colored either red or yellow with opposite faces always of the same color. Two dice are considered to have the same design if one of them can be rotated to obtain a dice that has the same numbers and colors on the corresponding faces as the other one. Find the number of distinct dice that can be designed. | ||
==Solution== | ==Solution== | ||
| − | |||
| − | |||
| − | |||
| − | |||
Latest revision as of 11:01, 2 September 2024
Problem 7
Unconventional dice are to be designed such that the six faces are marked with numbers from 
to 
with and 
appearing on opposite faces. Further, each face is colored either red or yellow with opposite faces always of the same color. Two dice are considered to have the same design if one of them can be rotated to obtain a dice that has the same numbers and colors on the corresponding faces as the other one. Find the number of distinct dice that can be designed.
