Answer to January 19, 2004 Problem
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| The Calendar Cube Problem |
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So you will need to build a calendar from two sets of cubes.
On the first set, spell the months with a letter on each face
of three cubes. Use lowercase three-letter English abbreviations
for the names of all twelve months (e.g., "jan", "feb", "mar").
On the second set, number the days with a digit on each face
of two cubes (e.g., "01", "02", etc.).
Show what letters and digits need to be put on the five cubes
so that you will be able to display all 366 days correctly!
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Solution to the Problem:
Cubes for the months:
a, e, l, t, u/n, v
Cubes for the dates:
0, 1, 2, 3, 7, 8
You have 12 months, with 19 unique letters.
Doing this, you find that you can only get rid of one letter,
either the "p" or the "d". You cannot do this with the "n" and "u"
since both of them are needed for June (jun).
With that, each month has one vowel -- even August, since you can easily substitute
the "n" for the "u". After this step it's mostly logic, since you now have 18 letters.
One of the easiest ways, then, is to start out with the "a" since the "a" cannot be on
the same cubes with the most letters (j n m r p y u g).
With the dates, 6 and 9 are reversible and you never need both of them at one time.
Nearly everyone sent in a different set of letters that worked, and James Alarie
sent in three different valid sets.
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| 1. Bob and Adam Arslan | Winchester, Virginia |
| 2. Jeffrey Gaither | Winchester, Virginia |
| 3. David & Judy Dixon | Bennettsville, South Carolina |
| 4. Akash Patel | Columbus, Georgia |
| 5. David Wong | Winchester, Virginia |
| 6. James Alarie | University of Michigan -- Flint, Flint, Michigan |
| 7. Kathryn Harris | Winchester, Virginia |
| 8. Patrick Wingfield | Winchester, Virginia |
| 9. Keith Mealy | Cincinnati, Ohio |
| 10. Britney Ford | Winchester, Virginia |
| 11. Walt Arrison | Philadelphia, Pennsylvania |
| 12. Shannon Bagshaw | Winchester, Virginia |
| 13. John Beasley | Winchester, Virginia |