Inspired from: Number Theory Class
Our magician was unhappy because his magic was revealed so fast! so he made another magic and gave a calculator to an audience and said:
- Pick any number,
- Multiply it with 23,
- Take the sum of its digits, let's call it A,
- Multiply the number you picked again with 67,
- Take the sum of its digits again, let's call it B,
- Take the difference of these two numbers as A-B, tell me the result!
The audience member said
Good, now remove any non-zero digit from your number and tell me the rest, and tell me the rest of digits in any order.
The audience member responded
$5$ and $2$.
And the magician announced in an instant,
The number you have removed was $9$.
The magician is right! How?