{"id":893,"date":"2022-02-24T19:51:55","date_gmt":"2022-02-24T22:51:55","guid":{"rendered":"https:\/\/numbers-magic.com\/?p=893"},"modified":"2026-02-01T02:45:03","modified_gmt":"2026-02-01T05:45:03","slug":"crazy-representations-of-natural-numbers-the-10958-problem","status":"publish","type":"post","link":"https:\/\/numbers-magic.com\/?p=893","title":{"rendered":"Crazy Representations of Natural Numbers \u2013 The 10958 Problem"},"content":{"rendered":"\n

In 2013-2014, author (click here<\/a>) wrote natural numbers in increasing and decreasing orders of 1 to 9 using only basic operations<\/strong>. See below some examples:\"crazy-2\"<\/p>\n\n\n\n

This work has been considered as \u201cImprobable Research\u201d<\/strong>. For details see the links:<\/p>\n\n\n\n

(i)  http:\/\/www.improbable.com\/2013\/02\/12\/lots-of-numbers-plain-and-almost-simple\/<\/a>;(ii) http:\/\/www.improbable.com\/2013\/06\/08\/lots-more-numbers-deemed-crazy-sequential\/<\/a><\/p>\n\n\n\n

Also refer Nebus 1<\/a>, Nebus 2<\/a>  for more comments. We observe that the number 10958<\/strong> 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<\/strong> and\/or factorial<\/strong> to write it. See below:<\/p>\n\n\n\n

10958<\/strong>:=1+2+3!!+(-4+5!+6-7)*89.<\/h3>\n\n\n\n

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

(i) The 10,958 Problem<\/a> \u2013 Numberphile \u2013 M. Parker; (2.970.174<\/strong>  views \u2013 till  22.10.21)
(ii)  A 10,958 Solution<\/a> \u2013 Numberphile \u2013 M. Parker. (1.552.751<\/strong> views- till 22.10.21)<\/p>\n\n\n\n

RUSSIAN TRANSLATIONS<\/strong><\/p>\n\n\n\n

(i) The 10,958 Problem<\/a> \u2013 Numberphile \u2013 M. Parker; (6.010.701 <\/strong>views \u2013 till 22.10.21)
(ii)  A 10,958 Solution<\/a> \u2013 Numberphile \u2013 M. Parker. (1.110.973<\/strong> views- till 22.10.21)<\/p>\n\n\n\n

Total views: 11.644.599<\/strong> till 22.10.21<\/p>\n\n\n\n

ALSO THIS NUMBER HAS BECOME A QUESTION OF DISCUSSION AT VARIOUS WEB-SITES. SEE THE LINKS BELOW:<\/h4>\n\n\n\n
  1. https:\/\/www.primepuzzles.net\/puzzles\/puzz_864.htm<\/a>;<\/li>
  2.  https:\/\/www.futilitycloset.com\/?s=10958<\/a>;<\/li>
  3. https:\/\/puzzling.stackexchange.com\/questions\/51129\/the-10-958-problem<\/a>;<\/li>
  4. https:\/\/puzzling.stackexchange.com\/questions\/47923\/rendering-the-number-10-958-with-the-string-1-2-3-4-5-6-7-8-9<\/a>;<\/li>
  5. https:\/\/www.reddit.com\/r\/mathematics\/comments\/6hooq2\/the_10958_problem\/<\/a>;<\/li>
  6. http:\/\/digg.com\/video\/10958-math-problem<\/a>;<\/li>
  7.  http:\/\/wssrmnn.net\/index.php\/2017\/04\/20\/the-10958-problem<\/a>;<\/li>
  8. https:\/\/twitter.com\/aap03102\/status\/854319054173220864<\/a>;<\/li>
  9. https:\/\/inderjtaneja.com\/2017\/12\/02\/10958-problem-1-5-millions-views<\/a>.<\/li>
  10. https:\/\/github.com\/nvalis\/10958<\/a>;<\/li>
  11. https:\/\/www.youtube.com\/results?search_query=10958<\/a>;<\/li>
  12. https:\/\/www.youtube.com\/watch?v=yCMvekktTa0<\/a>.<\/li><\/ol>\n\n\n\n

    EXTENSIONS<\/strong><\/h4>\n\n\n\n
    1. Extension to 11112-20000 \u2013 https:\/\/doi.org\/10.5281\/zenodo.2543626<\/a>;<\/li>
    2. Extension to 20001-25000 \u2013 Taneja-2<\/a> ;<\/li>
    3. Extension to 25001-30000 \u2013 Taneja-3.<\/a><\/li>
    4. Revised: 20001-3000: Crazy Representations of Natural Numbers From 20001 to 30000, Zenodo, February 3, 2019, pp. 1-276, http:\/\/doi.org\/10.5281\/zenodo.2556036<\/a><\/strong>.<\/li><\/ol>\n\n\n\n

      FURTHER EXTENSIONS<\/strong><\/p>\n\n\n\n