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Three Mathematicians standing on infinite ladder on step number 35, 192, 227 respectively.

Everyone has same two secret formula, based on current standing position(step Number) one of the formula calculates and tell individually a new and distinct step number.

All three Mathematicians have applied formula 13 times and managed to stand on the step number one

Can You Find Which Formulas They Have Used ?

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closed as too broad by Gareth McCaughan, Beastly Gerbil, Glorfindel, Sconibulus, greenturtle3141 Apr 9 '17 at 16:19

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ I believe this question may have more than one answer. $\endgroup$ – Oray Apr 9 '17 at 14:36
  • $\begingroup$ What is the source of this puzzle? $\endgroup$ – Gareth McCaughan Apr 9 '17 at 14:46
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    $\begingroup$ Two secret formulas? So one says what step to stand on next, and the other ... does what? $\endgroup$ – Gareth McCaughan Apr 9 '17 at 14:48
  • $\begingroup$ @gareth-mccaughan its based on one of the famous mathematical conjecture $\endgroup$ – Dharmesh Apr 9 '17 at 16:11
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    $\begingroup$ You're probably looking for the Collatz formula. This is still way too broad though - any number of things can be the "applied formula". $\endgroup$ – Deusovi Apr 9 '17 at 18:36
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Obviously the answer is that

each mathematician's formula is f(x) = 1. After applying this nine times they are all on step 1. [EDITED to add: when I wrote this, the question said 9 where it now says 13. But of course this answer works just as well with 13 as 9.]

Or, alternatively, we could close the question as too broad.

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  • $\begingroup$ f(x)=1 for n steps will surely gives any intended answer, but distinct value at each step which is one of the condition $\endgroup$ – Dharmesh Apr 16 '17 at 16:08
  • $\begingroup$ Distinct values at each step were not in the conditions when I wrote the answer above. $\endgroup$ – Gareth McCaughan Apr 17 '17 at 0:09
  • $\begingroup$ It was for the edited comment "But of course this answer works just as well with 13 as 9." $\endgroup$ – Dharmesh Apr 18 '17 at 11:12
  • $\begingroup$ Ah, OK. Then I didn't notice all the changes that had been made when the puzzle was edited. $\endgroup$ – Gareth McCaughan Apr 18 '17 at 14:16
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I have found an answer but I believe there are more than one answer.

There are two formulas, so the obvious way to use these formulas is standing on an even or odd ladder number. If you are on even ladder, use first formula, otherwise use second formula below.

The formulas are;

1- $n/2+2$ if n is even

and

2- $n+1$ if n is odd

and so the final step number is

6

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  • $\begingroup$ This would be one of the possible two formula for given question. can we use/tweak the same formula to take them all till step no #1 $\endgroup$ – Dharmesh Apr 9 '17 at 16:04
  • $\begingroup$ @Dharmesh you have changed to question a couple of times! (from 9 to 13, from any step no to 1...) $\endgroup$ – Oray Apr 10 '17 at 14:03

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