A rectangular wooden box measuring 8 cm by 5 cm by 2 cm is painted blue on all six faces and then cut into 80 cubes, each with an edge of 1 cm.

How many of these cubes are painted blue on exactly one of their faces?
Solution to the Problem:

Here is the solution:

The answer is 36 cubes.

The cubes form a 3 cm by 6 cm by 2 cm block in the central part of the block.


Colin Bowey sent in this diagram showing each block and how many sides were painted blue:



Correctly solved by:

1. Kamal Lohia Hisar, Haryana, India
2. Eva Hull Central High School,
Grand Junction, Colorado, USA
3. Dr. Hari Kishan D.N. College,
Meerut, Uttar Pradesh, India
4. Ivy Joseph Pune, Maharashtra, India
5. Colin (Yowie) Bowey Beechworth, Victoria, Australia
6. Johanna Villeda Central High School,
Grand Junction, Colorado, USA
7. Davit Banana Istanbul, Turkey
8. Dani-jo Ward Central High School,
Grand Junction, Colorado, USA
9. Raygan Ball Central High School,
Grand Junction, Colorado, USA
10. Dakoda Perrigo Central High School,
Grand Junction, Colorado, USA
11. Marely Lopez Serna Central High School,
Grand Junction, Colorado, USA
12. Leo Gutierrez Central High School,
Grand Junction, Colorado, USA
13. Yatzil Fregoso Central High School,
Grand Junction, Colorado, USA
14. Shyann Page Central High School,
Grand Junction, Colorado, USA
15. Justice Espinoza Central High School,
Grand Junction, Colorado, USA
16. Kelly Stubblefield Mobile, Alabama, USA