Crazy Representations of Natural Numbers – The 10958 Problem

In 2013-2014, author (click here) wrote natural numbers in increasing and decreasing orders of 1 to 9 using only basic operations. See below some examples:crazy-2

This work has been considered as “Improbable Research”. For details see the links:

(i)  http://www.improbable.com/2013/02/12/lots-of-numbers-plain-and-almost-simple/;

(ii) http://www.improbable.com/2013/06/08/lots-more-numbers-deemed-crazy-sequential/

Also refer Nebus 1, Nebus 2  for more comments. We observe that the number 10958 is the only number among 0 to 11111 that is not possible to write in terms of 1 to 9 in the increasing case. We need to use extra operations such as square-root and/or factorial to write it. See below:

10958:=1+2+3!!+(-4+5!+6-7)*89.

Numberphile produced two videos on YouTube using concatenation as an extra operation to bring representation of number 10958 in increasing order. See below both the links:

(i) The 10,958 Problem – Numberphile – M. Parker; (1.968.177 views – till  09.03.19)
(ii)  A 10,958 Solution – Numberphile – M. Parker. (1.118.495 views- till 09.03.19)

RUSSIAN TRANSLATIONS

(i) The 10,958 Problem – Numberphile – M. Parker; (2.237.434 views – till 09.03.19)
(ii)  A 10,958 Solution – Numberphile – M. Parker. (369.036 views- till 09.03.19)

Total views: 5.693.142 till 09.03.19

Also this number has become a question of discussion at various web-sites. See the links below:

(i) https://www.primepuzzles.net/puzzles/puzz_864.htm;

(ii)  https://www.futilitycloset.com/?s=10958;

(iii) https://puzzling.stackexchange.com/questions/51129/the-10-958-problem;

(iv) https://puzzling.stackexchange.com/questions/47923/rendering-the-number-10-958-with-the-string-1-2-3-4-5-6-7-8-9;

(v) https://www.reddit.com/r/mathematics/comments/6hooq2/the_10958_problem/;

(vi)  http://digg.com/video/10958-math-problem;

(vii)\ http://wssrmnn.net/index.php/2017/04/20/the-10958-problem;

(viii) https://twitter.com/aap03102/status/854319054173220864;

(ix) https://inderjtaneja.com/2017/12/02/10958-problem-1-5-millions-views.

Extensions

  1. Extension to 11112-20000 – https://doi.org/10.5281/zenodo.2543626;
  2. Extension to 20001-25000 – Taneja-2 ;
  3. Extension to 25001-30000 – Taneja-3

 

FURTHER EXTENSIONS

For the results among 11112 to 30000 see the following link:   https://zenodo.org/record/1998118

More work from Anne E. Bras and V.H.J. van der Velden see the following links:
– https://zenodo.org/record/2276623
– https://zenodo.org/record/2525823
– https://zenodo.org/record/2530025

More work from Anne E. Bras and V.H.J. van der Velden in different bases:

– https://zenodo.org/record/2530974 (= base 11, 0 up to AAAA, incomplete)
– https://zenodo.org/record/2530976 (= base 12, 0 up to BBBB, incomplete)
– https://zenodo.org/record/2530978 (= base 13, 0 up to CCCC, incomplete)
– https://zenodo.org/record/2530980 (= base 14, 0 up to DDDD, incomplete)
– https://zenodo.org/record/2530982 (= base 15, 0 up to EEEE, incomplete)
– https://zenodo.org/record/2530984 (= base 16, 0 up to FFFF, complete)
– https://zenodo.org/record/2536047 (= base 16, -FFFFF up to FFFFF, complete)
– https://zenodo.org/record/2531777 (= base 11 up to 15, now all completed)

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