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I was enjoying my lunch over the 8th episode of YuriYuri and right at the beginning there was this unusual calendar:

Truth be told, this is the first time I see a calendar like that. As you can see, it consists of 3 parts which seem to be made of wood. The lower part says "April", so I assume it is removable so that the cubes above it can rotate, and that there are 11 more like it somewhere else in store.

Now the tricky part is the numbers. The 2 blocks on top are set up to read "01" which is for April the 1st. But the top side of the block that reads 0 in front, has a 6 on it. What's going on? And there are only 4 sides that can be rotated with their front sides for each digit to form a number of a day of the month. Is this an animation mistake? If not, how can this calendar thingie work?

Also, is it even possible to make them read all numbers from 01 to 31?

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    I am going to guess that your assumption about there being 11 other month blocks is likely incorrect. I would imagine that the month block is long and skinny instead of short and fat. The month block is only 1/3 as deep as the day blocks. The 3 other long sides of the month block would have 3 other months. I am also going to guess that there are 2 other blocks with 4 months each immediately behind (that you can't see because they are covered up). This would account for all 12 months (3 blocks * 4 months) without the fear of losing any pieces because it's all contained within your picture. – WuHoUnited Dec 10 '14 at 23:39
  • You are asking about how a particular kind of calendar works. The scope of your question is off-topic in regards to the site, as defined in the help center. – Pteromys Dec 11 '14 at 5:53
  • @Pteromys the decision to ask this question was made in our chat room with enough reputable users online at the time. – Hakase Dec 11 '14 at 8:14
  • This picture confirms @WuHoUnited's suspicion. – Daniel Daranas Dec 11 '14 at 11:07
  • Bigger version of Daniel's pic – Hakase Dec 11 '14 at 11:28
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With two cubes, you don't have enough sides (total 12) to give both cubes numbers 0-9.

Instead, each cube has its own numbers (there may be other permutations that work, too):

  • One cube (A) will have 0, 1, 2, 4, 5, 6.
  • The other (B) will have 0, 1, 2, 3, 7, 8.

Then each date is represented by how the cubes are used:

  • 01-03: Cube A is 0, followed by cube B.
  • 04-06: Cube B is 0, followed by cube A.
  • 07-08: Cube A is 0, followed by cube B.
  • 09: Cube B is 0, followed by cube A, on 6, upside-down.
  • 10-13: Cube A is 1, followed by cube B.
  • 14-16: Cube B is 1, followed by cube A.
  • 17-18: Cube A is 1, followed by cube B.
  • 19: Cube B is 1, followed by cube A, on 6, upside-down.
  • 20-23: Cube A is 2, followed by cube B.
  • 24-26: Cube B is 2, followed by cube A.
  • 27-28: Cube A is 2, followed by cube B.
  • 29: Cube B is 2, followed by cube A, on 6, upside-down.
  • 30-31: Cube B is 3, followed by cube A.

And before you ask, no, I've never seen one of these, and thus I really have no citation. But given the fact that the cubes look like they can go in either order (since they have numbers on the side, they should come completely free), this seems like the most logical solution.

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    These do exist in real life (I had one at one point), and this is a correct description of how they work conceptually, though some might use different (but roughly equivalent) numbering patterns. – Logan M Dec 10 '14 at 22:05
  • @LoganM Is there a special name of such a calendar? – Gerret Dec 10 '14 at 23:22
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    Also, its typically made of 5 parts. Underneath the 2 cubes is a set of 3 blocks with 4 months each on them. You can't see the other two since they are underneath the cubes – Lawton Dec 10 '14 at 23:34
  • I've got one of these sitting on my desk, but I don't use it because it's so annoying to keep switching and rotating the cubes (which don't follow any particular pattern, unlike dice). Mine has also one cube for months (two on each face, only the top half shows) and a cube for day-of-week (two on each face, with 2.5 blank sides) – Bobson Dec 11 '14 at 2:31
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Are you sure they are cubes? If they are individual panels that 'flip', that 6 would be a 9 and it would make sense. Calendars that fip over like this do exist, so maybe it works like that and it's just not clear that it's supposed to flip.

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    If you look on the right side of the right cube, you can see that it's solid, and that there's no surfaces for flipping or any kind of hinged movement. – Killua Dec 11 '14 at 16:22

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