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A teacher on a foreign planet wants to make a classroom calendar out of cubic blocks. She wants to individually count each day by drawing a number on the faces of a block. There are 209 days in this planet's year, and she can draw any number (0-9) on each face.

For example, 19 would be:

 ---   ---
| 1 | | 9 |
 ---   ---

With a face on one block being 1, and the other block's face being 9.

Another example, 201, would be:

 ---   ---   ---
| 2 | | 0 | | 1 |
 ---   ---   ---

A face on one block would be 2, a second block's face being 0, and a third block with a face of 1.

What is the fewest amount of blocks she can use to count the days of the year (0-209), and what numbers are on each block?

All cubes must be used.

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  • $\begingroup$ Can you write on different faces of the same cube? $\endgroup$ – leoll2 May 2 '15 at 8:49
  • $\begingroup$ Yes. A single number may be drawn on each face. @leoll2 $\endgroup$ – Zach Gates May 2 '15 at 8:50
  • $\begingroup$ Ah great, Ill edit my answer now! $\endgroup$ – leoll2 May 2 '15 at 8:52
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My answer is

4 cubes

For each number, the same digit appears at most twice, except for 111, where 1 appears 3 times. Also, you can rotate the 9 to make 6, so after all we need 19 digits (2*9+3*1-2). For 19 digits the minimum is 4 cubes.
Cube #1: 012468.
Cube #2: 012568.
Cube #3: 01347.
Cube #4: 01357.

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  • $\begingroup$ I've edited the questions slightly. Can you give the numbers on each block's faces? $\endgroup$ – Zach Gates May 2 '15 at 9:03
  • $\begingroup$ Done, let me know if wrong $\endgroup$ – leoll2 May 2 '15 at 9:14
  • $\begingroup$ You have no way to make single digit days or double digits ending with zero. $\endgroup$ – Zach Gates May 2 '15 at 9:17
  • $\begingroup$ To make single digits, use only one cube! $\endgroup$ – leoll2 May 2 '15 at 9:27
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    $\begingroup$ Looks perfect! Nice job. $\endgroup$ – Zach Gates May 2 '15 at 10:00
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Since we're making upside down 6's be 9's, how about making upside down 2's be 7's? Depends on how good an artist the teacher is, but here's an example of it on a clock.

clock

Thus, my answer is

Three Cubes

The faces are:

123456
123480
125680

Edit: Didn't see that all cubes must be used. That makes it impossible to do with 3 cubes, unfortunately.

Double Edit: Actually, does the following configuration work? I can't find a number that I can't make...

012345
016823
014568

I feel like I'm missing something...

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  • $\begingroup$ +1 for a good attempt. I especially enjoyed your take on 2/7 flipping. $\endgroup$ – Zach Gates May 2 '15 at 9:56
  • $\begingroup$ Where are the seven? $\endgroup$ – leoll2 May 2 '15 at 10:00
  • $\begingroup$ @leoll2 The twos are also sevens! $\endgroup$ – VictorHenry May 2 '15 at 10:01
  • $\begingroup$ Upside 2, at most, is still a 2! $\endgroup$ – leoll2 May 2 '15 at 10:01
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    $\begingroup$ @leoll2 Check out the clock I linked, I think that upside-down 2 makes a pretty good seven! $\endgroup$ – VictorHenry May 2 '15 at 10:02

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