Solution

(related to Problem: Painting The Die)

The $1$ can be marked on any one of six different sides. For every side occupied by $1$ we have a selection of four sides for the $2.$ For every situation of the $2$ we have two places for the $3.$ (The $6, 5,$ and $4$ need not be considered, as their positions are determined by the $1, 2,$ and $3.$) Therefore $6, 4,$ and $2$ multiplied together make $48$ different ways — the correct answer.


Thank you to the contributors under CC BY-SA 4.0!

Github:
bookofproofs
non-Github:
@H-Dudeney


References

Project Gutenberg

  1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

This eBook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this edition or online at http://www.gutenberg.org. If you are not located in the United States, you'll have to check the laws of the country where you are located before using this ebook.