Let N be a positive integer. Suppose given any real x∈(0,1) with decimal representation 0.a1a2a3a4⋯, one can color the digits a1,a2,⋯ with N colors so that the following hold:
1. each color is used at least once;
2. for any color, if we delete all the digits in x except those of this color, the resulting decimal number is rational.
Find the least possible value of N.~Sutanay Bhattacharya
number theorycombinatorics