August 2023
Problem of the Month

Painted Cube Problem
Submitted by Brijesh Dave

A wooden cube n units on a side is painted red on all six faces and then cut into n³ unit cubes.

Exactly one-fourth of the total number of faces of the unit cubes are red.

What is n ?

Solution:

The answer is n = 4

Since there are n³ unit cubes and each cube has six faces, the total number of faces is 6 n³.

There are 6 n² faces that are painted red.

So, (1/4) (6 n³) = 6 n²

6 n³ = 24 n²

n = 4.

Correctly solved by:

1. K. Sengupta	Calcutta, INDIA
2. Rob Miles	Northbrook, Illinois, USA
3. Sudhir Bavdekar	Mumbai, India
4. Seth Cohen	Concord, New Hampshire, USA
5. Carlos de Armas	Barcelona City, Spain
6. Dr. Hari Kishan	D.N. College, Meerut, Uttar Pradesh, India
7. Colin (Yowie) Bowey	Beechworth, Victoria, Australia
8. Kamal Lohia	Hisar, Haryana, India
9. Kelly Stubblefield	Mobile, Alabama, USA

Send any comments or questions to: David Pleacher