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:

For more details and extension work by other see the following link:

- Inder J. Taneja, The Crazy Representations and 10958 Problem,
**https://inderjtaneja.com/2018/11/16/crazy-representations-of-natural-numbers-the-10958-problem/**

The above study include the natural numbers till 30000. In some case **factorials **and or **square-roots** are used.

Recently, author wrote the above numbers till 100000 in increasing and decreasing orders of 1 to 9 and 9 to 1 using only the idea of **factorials** along with basic operations. Below are few examples:

These numbers are written in four parts. See the links below:

- Inder J. Taneja, Crazy Representations of Natural Numbers From 20001 to 40000,
**Zenodo**, November 03, 2021, pp. 1-541,**https://doi.org/10.5281/zenodo.5642776**. - Inder J. Taneja, Crazy Representations of Natural Numbers From 40001 to 60000,
**Zenodo**, November 03, 2021, pp. 1-541,**https://doi.org/10.5281/zenodo.5642826**. - Inder J. Taneja, Crazy Representations of Natural Numbers From 60001 to 80000,
**Zenodo**, November 03, 2021, pp. 1-537,**https://doi.org/10.5281/zenodo.5642896**. - Inder J. Taneja, Crazy Representations of Natural Numbers From 80001 to 100000,
**Zenodo**, November 03, 2021, pp. 1-533,**https://doi.org/10.5281/zenodo.5642929**.

Recently, author wrote the numbers from 100001 to 200000 in increasing and decreasing orders of 1 to 9 and 9 to 1 using only the idea of **factorials** along with basic operations. Below are few examples:

These numbers are written in five parts. See the links below:

- Inder J. Taneja, Crazy Representations of Natural Numbers From 100001 to 120000,
**Zenodo**, November 03, 2021, pp. 1-541,**https://doi.org/10.5281/zenodo.5773381**. - Inder J. Taneja, Crazy Representations of Natural Numbers From 120001 to 140000,
**Zenodo**, November 03, 2021, pp. 1-541,**https://doi.org/10.5281/zenodo.5773384**. - Inder J. Taneja, Crazy Representations of Natural Numbers From 140001 to 160000,
**Zenodo**, November 03, 2021, pp. 1-537,**https://doi.org/10.5281/zenodo.5773386**. - Inder J. Taneja, Crazy Representations of Natural Numbers From 160001 to 180000,
**Zenodo**, November 03, 2021, pp. 1-533,**https://doi.org/10.5281/zenodo.5773388**. - Inder J. Taneja, Crazy Representations of Natural Numbers From 180001 to 200000,
**Zenodo**, November 03, 2021, pp. 1-533,**https://doi.org/10.5281/zenodo.5773390**.

The whole work is by use of basic operations along with **factorials**. There are few numbers not available by using **factorials**. In order to get the results we used an extra operation of **square-root**. These are following numbers:

These numbers are in increasing orders. Still there is one more numbers, i.e., **192398** not available even with **factorial** and **square-root**. We can get it alongwith other values by using **Triangular** number values and **factorial**. See below:

In case of decreasing orders we have all the numbers from 100001 to 200000.

The above study is extended to 300000 numbers, i.e., 200001-300000. Again the work is divided in five parts:

- Inder J. Taneja, Crazy Representations of Natural Numbers from 200001 to 220000,
**Zenodo**, January 08, 2022, pp. 1-529, https://doi.org/10.5281/zenodo.5831196 - Inder J. Taneja, Crazy Representations of Natural Numbers from 220001 to 240000,
**Zenodo**, January 08, 2022, pp. 1-534, https://doi.org/10.5281/zenodo.5831198 - Inder J. Taneja, Crazy Representations of Natural Numbers from 240001 to 260000,
**Zenodo**, January 08, 2022, pp. 1-532, https://doi.org/10.5281/zenodo.5831200 - Inder J. Taneja, Crazy Representations of Natural Numbers from 260001 to 280000,
**Zenodo**, January 08, 2022, pp. 1-537, https://doi.org/10.5281/zenodo.5831206 - Inder J. Taneja, Crazy Representations of Natural Numbers from 280001 to 300000,
**Zenodo**, January 08, 2022, pp. 1-535, https://doi.org/10.5281/zenodo.5831208

The whole work is by use of **factorial**, but there are only few numbers where we used extra operation as **square-root** and/or **triangular numbers**. In case of increasing order there are only 44 numbers, while in case of decreasing order there are only 14 numbers. See below these numbers:

Still a different kind of work is done by using the palindromic digits as 1357-9-7531, 2022-2202 etc. See the following links:

- Inder J. Taneja, Representation of Numbers from 1 to 20000 in Terms of Palindromic Digits 1357-9-7531, https://inderjtaneja.com/2022/01/06/representation-of-numbers-from-1-to-20000-in-terms-of-palindromic-digits-1357-9-7531/
- Inder J. Taneja, Representation of Numbers from 1 to 10000 in Terms of Palindromic Digits 2022-2202, https://inderjtaneja.com/2022/01/02/representation-of-numbers-from-1-to-10000-in-terms-of-palindromic-digits-2022-2202/

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