February 25, 2002
Problem of the Month
The Desk Calendar Problem
by Martin Gardner
A desk calendar consists of two cubes and cards with
the names of the months on them.
The day was indicated
by arranging the two cubes so that their front faces
gave the date.
The face of each cube bore a single digit,
0 through 9, and one could arrange the cubes so that their
front faces indicated any date from 01, 02, 03, ..., to 31.
One cube has a 1 and a 2 on it, and the other cube has a 3,
4, and a 5 on it.
Determine the missing four numbers on the
first cube and the missing three digits on the second cube.
It is a bit trickier than one might expect.
Solution to the Problem:
The first cube consists of 0, 1, 2, 6, 7, and 8.
The second cube consists of 0, 1, 2, 3, 4, and 5.
The 6 on the first cube can also be used as a 9, which
will give you all the combinations from 01 to 31.
Correctly solved by:
| |
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| 2. Keith Mealy **
|
Cincinnati, Ohio
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| 3. Rick Jones
|
Kennett Square, Pennsylvania
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| 4. Richard K. Johnson
|
La Jolla, California
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| 5. James Alarie
|
University of Michigan -- Flint, Michigan
|
| 6. Renata Sommerville
|
Austin, Texas
|
| 7. David and Judy Dixon *
|
Bennettsville, South Carolina
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| 8. Bahareh Joukar
|
Winchester, Virginia
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| 9. Tori Eads
|
Winchester, Virginia
|
| 10. ----------
|
United Kingdom
|
| 11. Anne Beavers
|
Arlington, Virginia
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| 12. Elizabeth Emmart
|
Winchester, Virginia
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| 13. Rich Murray
|
Ridgetown, Ontario, Canada
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| 14. Andrea Flandry
|
Columbus, Georgia
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| 15. John Beasley
|
Winchester, Virginia
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| 16. John Funk
|
Ventura, California
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| 17. Ellen Sankovich
|
Winchester, Virginia
|
| 18. Janine Oliver
|
Winchester, Virginia
|
| 19. Griffin
|
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| 20. Kim Schmidt
|
Rockford, Michigan
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| 21. James Shuster
|
Rockford, Michigan
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| 22. Keeley Mills
|
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| 23. Vanessa Kargenian
|
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|
* David and Judy Dixon also created two other cubes which would
give all the possible dates from 01 to 31:
1st cube: 0, 1, 2, 3, 7, 8
2nd cube: 0, 1, 2, 4, 5, 6
** Keith Mealy sent in his design for a cube on which you can get
the 7 days of the week:
Su, M / W (inverted), Tu, Th, F, Sa