Because these have been so successful in the past, I had to bring up my own. In fact, this puzzle was inspired by Find the next number even though I (and I guess everybody but the author) still don't know the intended solution yet. Anyway, here it is:

The puzzle

The British inventor Jackemias Muff invented (and build) a number-evolving machine in 1817. (It was a cold, windy winter's day in Manchester, the Sunday before boxing-day.) You could feed it with any number, and it would produce an unambiguously determined, endless series of follow-up numbers.

For example, if you feed it with "8" you would get


If you feed it with "28" instead, you would get


Can you explain how his machine works and build a copy?

Victory condition: A correct answer is able to reproduce both series starting from the same seed values and can successfully predict the next number in each series.

I do not have proof that Muff's machine is unique, although I believe it is.

I will add hints over time, one is given as a starter:

In 1817, computers have not yet been invented. (Well, 'computer' was still a job-description those days..)

  • 4
    $\begingroup$ Just going for the victory condition: var input = window.prompt('Feed me'); var output = []; output[8] = '8,5,10,14,23,36,47,59,70,78,84,96,'; output[28] = '28,12,19,28,41,51,61,71,83,96,'; while (true) console.log( output[ input ] ); :-) $\endgroup$
    – Joe
    Nov 27, 2014 at 14:14
  • $\begingroup$ @Joe So you predict that the next numbers are...? $\endgroup$ Nov 27, 2014 at 14:15
  • 2
    $\begingroup$ @No.7892142 the number you input. It just loops. Before anyone gets upset, there's a reason it's a comment and not an answer ;-) $\endgroup$
    – Joe
    Nov 27, 2014 at 14:15
  • $\begingroup$ +1 for not just skipping any number-series puzzle. ;-) (But wrong answer ;->) $\endgroup$
    – BmyGuest
    Nov 27, 2014 at 14:16
  • 1
    $\begingroup$ @skv: :c) Pretty, actually. But I will accept any valid solution and I would LOVE to see one which isn't mine. $\endgroup$
    – BmyGuest
    Nov 27, 2014 at 14:24

1 Answer 1


The sequence is generated as follows:

Each consecutive term is except for the first (5 and 12 respectively) term is made by adding 1 and the length of the text representation of the current number to the current number. The 5 and 12 are made by simply counting the length of the text representation of the first term.


Next terms will be 107

First sequence:

8 -> "eight" -> 5
5 -> 5 + len("five") + 1 -> 10
10 + len("ten") + 1 -> 14
14 + len("fourteen") + 1 -> 23
Next steps are obvious.

  • $\begingroup$ I knew it would be too easy :c) $\endgroup$
    – BmyGuest
    Nov 27, 2014 at 14:57
  • $\begingroup$ Nicely spotted! $\endgroup$ Nov 27, 2014 at 15:00
  • $\begingroup$ @BmyGuest It was one of those which you either solve on the spot or you don't at all. Nice one though :) $\endgroup$
    – dmg
    Nov 27, 2014 at 15:04
  • $\begingroup$ a machine that counts keys, computes adding by 1 and shows the result with other keys representing digits... in 1817... ok $\endgroup$
    – kokbira
    Nov 27, 2014 at 18:49
  • 2
    $\begingroup$ @kokbira as with most machines from that time: when you opened the cupboard underneath you'd have found an Indian dwarf with a big brain and a fast handwriting.... $\endgroup$
    – BmyGuest
    Nov 27, 2014 at 19:07

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