Calendar Cubes

[Karolina82]

A calendar showing the days of the month is made up of two cubes. What digits need to be drawn on both cubes so that any day of the month can be shown ? How many different solutions are there ?

[Buenchico]

Answered here:
https://puzzlersworld.com/interview-puzzles/calendar-cube/

as well as here:
http://www.techinterview.org/post/508822718/calendar-cubes/

and here:
http://www.braingle.com/brainteasers/teaser.php?op=2&;id=48373&comm=0

[Karolina82]

Thank you Buenchico. I have two such calendars at home.

[JJ109]

None of Buenchico's answers give you the answer to part 2

As specified both cubes must contain 0,1,2 to cover instances of 11, 22 and 03,04,05,06,07,08,09
The 6 can be turned upside down to represent 9
Therefore so far you have 012 on both cubes and you must place the other 6 numbers (3,4,5,6,7,8) in the remaining 6 spaces
How many ways can you do this?
In maths combinations terms, the answer is 6C3 or choose any 3 from 6.
6C3 = 6! / 3!x3! = 720 / 6x6 = 720 / 36 = 20
Answer = 20 ways
eg cube 1 with 012 + 345, 346, 347,348, 356, 357,358
367,368,378, 456, 457, 458, 467, 468, 478, 567, 568, 578, 678
Obviously you do not need to bother about cube 2 as it will be filled with 012 and whichever 3 numbers are not on cube 1

Answer = 20 solutions
The answer is 6C3 or

[Karolina82]

Thank you JJ109. I could not have calculated the number of solutions due to my shortcomings in mathematics. However you have explained it very clearly and I was able to follow it.

[JJ109]

You're most welcome