Does anyone know how to create a perpetual calendar on the sides of five dice ? The calendar is required to show just two digit day, and three letter month name. Apparently this can be done using French month names - i.e. (JAN FEV MAR AVR MAI JUN JUI AOU SEP OCT NOV DEC) but not possible using English three letter month names. I have tried this, and it just seems a misery of endless tinkering. Is there a method in it somewhere ?
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Good point - thanks very much. PS Z also not needed - but that does not affect the point of the argument. Thanks again. – Charles Bowyer Nov 01 '15 at 18:23
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Obviously this is not an answer to the question (which is why it is here in a comment), but one English-language solution seems to be to use the orientation of the face of the die to select among 12 months on just one die: https://www.momastore.org/museum/moma/ProductDisplay_Cubes%20Perpetual%20Calendar_10451_10001_162596_-1_26674_11527_102669?gclid=Cj0KEQiA0-GxBRDWsePx0pPtp4sBEiQACuTLNhuKIB5_4nuFR9vSufmSsZ6CY3l8GKnM4-Ndk7Ccmq0aAu-S8P8HAQ – David K Nov 03 '15 at 12:40
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For the English three letter abbreviations of the months we need 19 different letters (only H, I, K, Q, W, X, Z are not needed), one more than the $18$ available faces on three dice. Maybe we could cheat a little, as with $6$ and $9$ on the digits dice. But there is another point: The graph $\Gamma$ containing the $19$ occurring letters as vertices, and an edge for any two letters that should not appear on the same die, contains a $K_4$ consisting of A, J, N, and U; see the figure below. Therefore we need at least four dice to deal with the letters of such a calendar. A way out could be the following: Introduce a sixth die allowing for a slash: JAN/15. Now the problem becomes again interesting, and it is not too difficult to devise a solution. Of course we have to cheat a little and use the $6$ for a $9$ as well. The six dice could show the following entries:
(0,1,2,3,4,5), (0,1,2,6,7,8),
(A,E,T,V,/,*), (B,M,P,O,U,/), (C,L,N,R,S,/), (D,F,G,J,Y,/).
The * denotes a free space for the logo of the manufacturer. The four-coloring of $\Gamma$ shown in the following figure was set up in such a way that no color occurs more than five times, allowing for a slash on each letter-die.
Christian Blatter
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