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A math brain teaser from me

There is a smart people's club you want to enter. The bouncer has a secret number that is an integer between 1 to 15.

You tell a number to him. If it is correct, he opens the door.

If your number is wrong, he will change the secret number by doing:

  1. Compute:

    , where n is greater number of the secret number and your number. m is the other of the two.

  2. Double the number k from Step 1, then divide by 15. Keep the remainder.
  3. Repeat Step 2 until the bouncer gets tired of it.

If the number at the end of Step 3 happens to be 0, he will change it to 15. Otherwise, no more operation. This number will be the new secret number you have to guess.

Come up with the number sequence you will try so that you can get in the club as soon as possible.

The bouncer takes no bribe. No one else tries between your trials.

Original post: Jan. 27, 2013 | Last updated: Jan. 27, 2013

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