Question 934615
ANSWER:
Counting only positive integers (not counting zero),
there are {{{9^6-1=531441-1=highlight(531440)}}} numbers less than 1 million that do not contain the digit 2.
If we count zero, then it is just {{{531441}}} .
 
EXPLANATION:
Counting zero, numbers less than 1 million can be considered sequences of 6 digits,
{{{0 ="000,000"}}} , {{{1="000,000"}}} , ..... {{{"999,999"}}} ,
so there are {{{10}}} possible choices for each digit position,
and as a consequence {{{10*10*10*10*10*10=10^6="1,000,000"}}} .
If we do not count {{{0 ="000,000"}}} , then there would be {{{1}}} less.
If we cannot use the digit {{{2}}} ,
there are only {{{9}}} choices for each digit position,
and we get {{{9^6=531441}}} 6-digit sequences made from the digits 0,1,3,4,5,6,7,8,9,
including {{{"000,000"}}} , which represents the number {{{0}}} .