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Some mathematical magic

Puzzling Asked by quarague on June 15, 2021

The magician will perform some mathematical magic.
He asks his guest to secretly pick any two digit number and then perform a number of operations on it.

  1. If the number is even, divide by 2, if it is odd subtract 3 and then divide by 2.
  2. Multiply by 3.
  3. Add 5.
  4. If the number has 3 digits, subtract 102.
  5. Multiply by 6.
  6. Subtract 21.
  7. Compute the sum of the digits and continue with this sum. For example if you have 41, continue computing with 5=4+1. *
  8. If the number has only a single digit, multiply by 2.
  9. Subtract 5.

At this point, the magician reveals the number the guest arrived at after step 9.

How does this trick work?

Edit: * As noted in the comments, it can happen that you have a negative number at this point. In this case just ignore the minus sign in front. So for example the sum of digits of -16 would be 7.

One Answer

The number chosen is somewhere between $10$ and $99$.

So the final answer is

Correct answer by Rand al'Thor on June 15, 2021

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