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Given a Rubik's Cube pattern:

enter image description here

And using each of the following 12 pentominoes at least once:

enter image description here

Can you cover entirely the Rubik's Cube?

The answer is obviously yes! However, given that the Rubik's Cube pattern has 9x6 = 54 squares and the 12 pentominoes represent 60 squares, there will be, at the least, 60-54 = 6 squares outside the Rubik's Cube pattern!

How many squares outside the pattern can you have at minimum?

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    $\begingroup$ You must have played a much harder version of Tetris than I'm familiar with ;-) $\endgroup$ Commented Jul 13 at 0:15
  • $\begingroup$ Shouldn’t it be called pentris? $\endgroup$ Commented Jul 13 at 0:32
  • $\begingroup$ @Pranay No, we really should just call them pentominoes. $\endgroup$ Commented Jul 13 at 5:52
  • $\begingroup$ @DanielMathias. I agree, but it’s better than calling it Tetris. $\endgroup$ Commented Jul 13 at 6:08

1 Answer 1

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The minimum number of extra squares is

six; place the missing T wherever you like.
enter image description here

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    $\begingroup$ Wow - how in the world did you find this ? What was your approach to the problem ? $\endgroup$ Commented Jul 14 at 9:35
  • $\begingroup$ Repeated trial and error, using the two pentominoes on the left as a starting point. I knew from the beginning what the correct number of extra cells would be, since the possible numbers are so restricted, so I just needed to find a good place for them. $\endgroup$ Commented Jul 14 at 14:15

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