I saw an interesting calendar in a shop. It is composed of two cubes with numbers written on their 6 sides. By placing these cubes side by side one can make any day of the month from 1 to 31 (even 32). This tickled my mathematical curiosity and made me wonder: what is the largest contiguous range of numbers you can make with 3 cubes? Bonus question: what happens if you allow cubes to be flipped, so 6 can become 9 and vice versa?
This problem is similar to this Counting numbers with 3 dice but here we don't require 0-padding, so the answer is different. For example, here we can use a single die to represent single-digit numbers.