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