__unit__cubes are glued together to form a cuboid . A pack, containing 2009 stickers, is opened, and there are enough stickers to place 1 sticker on each exposed face of each unit cube.

How many stickers from the pack are left?

Kindly provided by UKMT 2009
unit cubes are glued together to form a cuboid. A pack, containing 2009 stickers, is opened, and there are enough stickers to place 1 sticker on each exposed face of each unit cube.How many stickers from the pack are left?
17 Comments
Vera Cherepinsky
3/9/2014 08:55:00 am
SPOILER ALERT - Solution below
Reply
Tom Thomson
3/9/2014 10:28:52 am
The only cuboids that can be built from 2009 unit cubes measure
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Paul
3/9/2014 10:57:10 pm
Thorough, as always, Tom. Thanks again.
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Jim Walker
3/9/2014 11:16:36 am
Factor 2009 = 7*7*41 meaning the cuboid must have these dimensions. The surface area of the cuboid is 1246. Subtracting from 2009 leaves 763 unused stickers.
Reply
3/9/2014 01:25:44 pm
Being a pedant, I have to go with Tom Thomson's answer. The other configurations ARE cuboids, after all.
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Rand Wise
3/9/2014 07:00:51 pm
Tom forgot one case (1 X 41 X 49), but it also too large.
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Tom Thomson
4/9/2014 11:21:52 am
Drat!
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brian
3/9/2014 10:02:32 pm
Dang, everyone is right!
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Dave
4/9/2014 07:46:00 am
I also had 763 for an answer. We are all correct!
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Ken
6/9/2014 08:05:31 am
An obvious extension of this problem is to ask how many stickers are left over if we put one sticker on each exposed cube (ans = 975).
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Tom Thomson
6/9/2014 08:56:51 am
I imagine we'll all agree on that one too, since the interior cubes of a cuboid array of 7 X 7 X 41 cubes contains 5 X 5 X 39 of those cubes, and 5*5*39 is 975.
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Tom Thomson
6/9/2014 09:02:57 am
All those "there was an error in subtting you reply" messages in red led me to repeat (with variations in case it was a text-specific issue). The result is a silly number of comments saying the same thing. I'm sory for teh redundancy, but definitely i claim that it ws not my fault - the site gave an error message and didn't diplay the comment until the last time, when it gave no error message and displayed all the previous attempts as well as the final one.
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Paul
6/9/2014 11:50:11 pm
Hi Tom. I'll look into this and see what can be done. Thanks.
Reply
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