A businessman has two cubes on his desk. Each cube has a number on each of its sides. Every day, the businessman arranges the cubes in such a way that the upward facing numbers display the day's date.
(Note that both cubes are always used for this, so on the 7th of the month, the cubes' surfaces display "07".)
How are these cubes numbered? (I.E. What numbers are on which cube?  call them C_{1} and C_{2}.)
(From http://www.ocf.berkeley.edu/~wwu/riddles/intro.shtml)
Each cube must have a 1 and a 2 (to account for the 11th and the 22nd) When assigning the other numbers, it quickly becomes apparent that there must also be a 0 on each cube in order that each number from 3 to 9 can be paired with a 0. This accounts for six of the twelve faces of the two cubes. The other numbers can be assigned randomly between the two other six faces  except that S = {3, 4, 5, 6, 7, 8, 9} has seven members, not six.
At this point we have to cheat. It is necessay to choose a font for the numbers so that the 6 and the 9 are identical except for the orientation. Then we assign faces to each of the digits from 3 to 8. There is no cube face with the digit 9, but on the 09th, the 19th, and the 29th, the businessman displays 06, 16 or 26 with the 6 upsidedown.

Posted by TomM
on 20020909 20:12:27 