As part of simple card trick, I want to allow a user to choose a number between 1 and 100 and then ask them to do various maths to lead them to the same number so their choice becomes irrelevant.

One way to do this is ask them to multiply their chosen number by 9. Then ask them to repeatedly sum each individual digit until they get to a single digit number. This will always come back to 9 and thus you have a base to then transition to the desired number.

Are there any other ways to do this (ideally something a bit more subtle)


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    $\begingroup$ Darn. Emil changed the tag (from central-simple-algebra) just as I was about to make a suggestion involving computation of Brauer groups. $\endgroup$ – Steven Landsburg Dec 15 '14 at 16:52
  • $\begingroup$ Sorry about that :) $\endgroup$ – Emil Jeřábek Dec 15 '14 at 16:57
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    $\begingroup$ I am reminded of a story about one of my former professors, who was years ago reprimanded by some sort of communist party committee for working on boundary value problems, on the grounds that every scientist should strive to work on central problems. $\endgroup$ – Emil Jeřábek Dec 15 '14 at 17:04
  • $\begingroup$ See en.wikipedia.org/wiki/Collatz_conjecture. Ask them to run the computations until they stabilise. Definitely works for integers $\le 100$, and conjecturely for arbitrary positive integers. (Oops, I just remembered that it always ends in $\ldots,4,2,1,4,2,1,\ldots$; so maybe this is not a very good idea. $\endgroup$ – jmc Dec 15 '14 at 17:36
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    $\begingroup$ I really really want to know who upvoted this one. $\endgroup$ – Steven Landsburg Dec 15 '14 at 23:04

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