MathDB

A toymaker has

k

dice at his disposal, each with

6

blank sides. On each side of each of these dice, the toymaker must draw one of the digits

0, 1, 2, \ldots , 9

.
Determine (in terms of

k

) the largest integer

n

such that the toymaker can draw digits on the

k

dice such that, for any positive integer

r \leq n

, it is possible to choose some of the

k

dice and form with them the decimal representation of

r

.
Note: The digits 6 and 9 are distinguishable: they appear as 6 and 9.

Problem Statement