You can still buy them, so there must be some enduring appeal. The calendar interested

*me*because of a strange quirk that isn't immediately obvious.

There are four blocks: one for the day of the week (with seven labels), two for the day of the month (1 to 31) and one for the month (with twelve labels). The "weekday" and "month" blocks are easy to label. For example, two months on each face fills the "month" block and, providing the container covers up the lower half of the block, all is peachy.

The two date blocks are a little more involved. Dates run from "01" to "31":

01,02,03,04,05,06,07,08,09,10,

__11__,12,13,14,15,16,17,18,19,20,

21,

__22__,23,24,25,26,27,28,29,30,31By inspection, we see that the only digits that appear twice on a single date are "1" and "2". However, if you sit down with a pencil and paper, it quickly becomes apparent that you'll also need two zeroes. That means that the following digits are required:

0,0,1,1,2,2,3,4,5,6,7,8,9

But, hang on! That's thirteen digits. Two cubes have only twelve faces between them. How do they fit? The clever "quirk" is that "6" and "9" occupy the same face; you simply flip the block around 180 degrees. This gives you the following faces for the two blocks:

0,1,2,3,4,5

0,1,2,6,7,8

Fast forward several years, if not decades, and my current fascination with clocks led me to consider whether you could tell the time with a similar arrangement. I knew representing the hours would not be a problem: as we've seen, two blocks can represent all integers between "00" to "23" inclusive for a twenty-four-hour clock. But representing minutes is harder.

It is fairly obvious that you need

*at least*three blocks to represent all integers between "00" to "59" inclusive. But are three

*sufficient*? It turns out that they

*are*; you don't even need to use the upside-down "9" trick. The solution uses an additional cube to display a colon between the hours and minutes digits. For example:

23:59

:,0,1,2,3,4

:,5,6,7,8,9

hours-a 0,1,2,3,4,5

hours-b 0,1,2,6,7,8

minutes-a :,0,1,2,3,4

minutes-b 0,1,2,3,4,5

minutes-c :,5,6,7,8,9

seconds-a :,0,1,2,3,4

seconds-b 0,1,2,3,4,5

seconds-c :,5,6,7,8,9

hours-a <=> hours-b

minutes-a <=> minutes-c

seconds-a <=> seconds-c

Some extra fettling is needed to make the rotations aesthetically pleasing, but the result is a twenty-four-hour clock that twists and turns at a fair old lick.

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