Think numbers not dots!
Problem: (from eon)
A simple little puzzle. Suppose you are given two ordinary 6 sided dice. Is it possible to put the numbers 0-9 (with repetition) onto the faces of both dice, such that using both dice you can display all the days of the month i.e. 01 – 31 .
Cant be done.
My reasoning is as follows. Each of the dice must have a 1 and 2, in order to denote 11 and 22. This leave 4 spaces on each die, which in order to denote 01 – 09, we must put a 0 on each of the dice. This leaves 3 space on each die, which if we only but the remaining numbers 4 – 9 (7 total), will not fit in the remaining six places.
Is there a more elegant proof?
I am wrong. It can be done. So can anyone figure out why I am wrong? No cheating by checking out the response by tpc.