A magician said to an audience member:
- Pick a number,
- Double it,
- Add $7$,
- Multiply it by $5$,
- Subtract the number you started with,
- Remove any non-zero digit from the answer,
and then tell me the remaining digits in any order.
The audience member said
$6$ and $8$.
And the magician announced,
The digit you removed was $3$, right?
The magician is right! Why? Justify!