How many six-digit numbers do not have adjacent digits the same? That is, we are excluding numbers like $689113$.
Source: NCTM Mathematics Teacher

SOLUTION
Let $abcdef$ represent the six-digit numbers.
Choices for $a=\left \{any\;digit\;except\;0\right \}\rightarrow 9$ choices
Choices for $b=\left \{any\;digit\;except\; a\right \}\rightarrow 9$ choices
Choices for $c=\left \{any\;digit\;except\; b\right \}\rightarrow 9$ choices
Choices for $d=\left \{any\;digit\;except\; c\right \}\rightarrow 9$ choices
Choices for $e=\left \{any\;digit\;except\; d\right \}\rightarrow 9$ choices
Choices for $f=\left \{any\;digit\;except\; e\right \}\rightarrow 9$ choices
Total count of six-digit numbers that do not have adjacent digits the same
$9\times 9\times 9\times 9\times 9\times 9=531441$

Answer: $531441$