Today From Bedtime Math: A Toy for Your Fingers or Feet

When you&re a great Rubik&s cuber, it only takes 5 seconds to set a world record. Get your fingers flying in this Bedtime Math challenge!
By Laura Overdeck
Sep 08, 2015

Ages

3-13


Sep 08, 2015
The Rubik's cube is a simple idea that's really hard to do. The cube's 6 colorful faces are each divided into 3 rows and 3 columns that can spin. You turn the sections to mix up the colors, then try to unscramble the squares to make each side all one color again. People have solved the cube at crazy-fast speeds: Collin Burns' world record is 5 and 1/4 seconds! But at the Rubik's Cube World Championship in Brazil in July, people did even wackier tricks. Jakub Kipa solved the cube using his feet, in just 20 seconds. Other people solve it blindfolded: they stare at the cube to remember where all the colored squares are, then shut their eyes and solve it just from memory. Erno Rubik, the inventor of the cube, must be wowed by all this: he says it took him a month to solve his own cube the first time!
 
Now see if you and your kids can come up with the solutions to these math challenges:
 
Wee ones: Do you see any cube or other rectangular box in the room? Count its "faces," or flat sides. How many does it have? Don't forget the bottom!
 
Little kids: If you've unscrambled 4 of the cube's 6 faces, how many more do you have left to solve?  Bonus: If Jakub can solve the cube in 20 seconds and Collin can in 5 seconds, how much faster are Collin's hands than Jakub's feet?
 
Big kids: The top layer of the cube has 9 pieces, or chunks of plastic, as does the bottom layer; the middle layer adds another 4 center pieces and 4 edge pieces. If all the corner chunks and center pieces on each face are correct, how many pieces are left to solve?  Bonus: The cube has 3 rows of 3 squares on each face – and then it has 6 faces. How many little squares does it have in total?
 
The sky's the limit: If on the blue face you've gotten 7 blue squares and 2 yellow squares, how many different ways could those 2 yellows be lined up?
 
Answers:
Wee ones: All cubes (and any rectangular boxes, called "prisms") have 6 faces each.
Little kids: 2 faces.  Bonus: 15 seconds faster.
Big kids: 12 pieces. There are 26 pieces in total, and the cube has 8 corners and 6 centers (14 solved), leaving 12 edges.  Bonus: 54 squares.
The sky's the limit: 36 ways. This is a "n choose x" problem, in this case choosing 2 from 9. If the very 1st square is yellow, the 2nd yellow has 8 other spots it could go. Then start over – now if the 2nd is yellow, there are just 7 other places for the 2nd yellow, since you already covered having yellow in the first spot. Then if the 3rd is yellow, you have 6 new spots, and so on…giving you 8+7+6+5+4+3+2+1, or 36 possible pairs.
 
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