A classic children's toy consists of 12 different blocks that combine to form a rectangle showing a man's face. Each block has four sides with alternatives for that part of the face; for example, the block for the right eye might have a closed eye on one side, a partially open eye on another, and so on. A child can turn any block and so change that part of the face, and in this way many different faces can be formed.

If a child makes one change each minute and spends 49 hours a week changing faces, how many years will it take to see every possible face? (Round your answer to the nearest whole number.)


How many years?

 Feb 24, 2018

The number of possible "faces"  is


4^12  = 16,777,216


The number of minutes spent each year is 


 49 hours per week* 60 minutes per hour * 52 weeks per year   =  152880 min per yr


So...the number of years is :


16777216 / 152880  ≈  109.7 years  =  110 years



cool cool cool

 Feb 25, 2018
edited by CPhill  Feb 25, 2018
edited by CPhill  Feb 26, 2018

Okay thanks I'm following how you solved but I type that answer in and it said it was wrong. In the back of my textbook they have the same problem only difffernce is 48 hours instead of 49.  They got 28 years. They do not show any work in the book though.

Guest Feb 25, 2018

I'm not sure, then.....maybe someone else can spot my error  or have another way to solve this...



cool cool cool

CPhill  Feb 25, 2018

You where right on your setup, but the fianl answer ended up being 109 years.

Guest Feb 25, 2018
edited by Guest  Feb 25, 2018
edited by Guest  Feb 27, 2018

Answer to this question


109 years.


Found that out looking at the answer key after the assignment was turned in.

 Feb 27, 2018

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