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 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:

1. Chip Schweikarth Winchester, Virginia
2. Keith Mealy ** Cincinnati, Ohio
3. Rick Jones Kennett Square, Pennsylvania
4. Richard K. Johnson La Jolla, California
5. James Alarie University of Michigan -- Flint, Michigan
6. Renata Sommerville Austin, Texas
7. David and Judy Dixon * Bennettsville, South Carolina
8. Bahareh Joukar Winchester, Virginia
9. Tori Eads Winchester, Virginia
10. ---------- United Kingdom
11. Anne Beavers Arlington, Virginia
12. Elizabeth Emmart Winchester, Virginia
13. Rich Murray Ridgetown, Ontario, Canada
14. Andrea Flandry Columbus, Georgia
15. John Beasley Winchester, Virginia
16. John Funk Ventura, California
17. Ellen Sankovich Winchester, Virginia
18. Janine Oliver Winchester, Virginia
19. Griffin -----------
20. Kim Schmidt Rockford, Michigan
21. James Shuster Rockford, Michigan
22. Keeley Mills -----------
23. Vanessa Kargenian -----------
* 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