# Crazy Representations of Natural Numbers – The 10958 Problem

#### ByInder J. Taneja

Feb 24, 2022

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:

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

Also refer Nebus 1Nebus 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; (2.970.174  views – till  22.10.21)
(ii)  A 10,958 Solution – Numberphile – M. Parker. (1.552.751 views- till 22.10.21)

RUSSIAN TRANSLATIONS

(i) The 10,958 Problem – Numberphile – M. Parker; (6.010.701 views – till 22.10.21)
(ii)  A 10,958 Solution – Numberphile – M. Parker. (1.110.973 views- till 22.10.21)

Total views: 11.644.599 till 22.10.21

#### 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.
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.

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)

#### By Inder J. Taneja

##### 23 thoughts on “Crazy Representations of Natural Numbers – The 10958 Problem”
1. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

2. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

3. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

4. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

5. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

6. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

7. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

8. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

9. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

10. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

11. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

12. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

13. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

14. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

15. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

16. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

17. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

18. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

19. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

20. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

21. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

22. […] Crazy Representations of Natural Numbers – The 10958 Problem […]

23. […] Crazy Representations of Natural Numbers – The 10958 Problem […]