Question 4
A positive integer $n$ is called solitary if,
for any non-negative integers $a$ and $b$ such that $a+b=n$,
either $a$ or $b$ contains the digit $1$.
Determine, with proof, the number of solitary integers less than $10^{2026}$.
Proposed by Carl Schildkraut.
Manual essay; 1 editorial point, not official contest scoring. Automatic answer fields are intentionally empty.
for any non-negative integers $a$ and $b$ such that $a+b=n$,
either $a$ or $b$ contains the digit $1$.
Determine, with proof, the number of solitary integers less than $10^{2026}$.
Proposed by Carl Schildkraut.
Manual essay; 1 editorial point, not official contest scoring. Automatic answer fields are intentionally empty.