http://i1068.photobucket.com/albums/u446/Littledogstar/SAM_3467_zpsgmwehx8e.jpg

This desk toy made me wonder what the largest number, M, is which can be displayed by arranging two six sided dice of which any given side may contain a number from 0 to 9 such that any whole number from 01 to M can also be built.

Obviously the maker of the toy has solved the problem up to 31 - a date that comes along every two months or so - but can you go bigger?

(Hint: It won’t be 99 because there will be some numbers smaller than 99 that cannot be built.)

Rigil[b]

ETA: Just noticed that six and nine are one and the same symbol … just to make it infernally interesting. [/b]>:D