<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Throughout history, recreational mathematics has always played a prominent role in advancing research. Following in this tradition, in this paper we extend some recent work with crazy sequential representations of numbers− equations made of sequences of one through nine (or nine through one) that evaluate to a number. All previous work on this type of puzzle has focused only on base ten numbers and whether a solution existed. We generalize this concept and examine how this extends to arbitrary bases, the ranges of possible numbers, the combinatorial challenge of finding the numbers, efficient algorithms, and some interesting patterns across any base. For the analysis, we focus on bases three through ten. Further, we outline several interesting mathematical and algorithmic complexity problems related to this area that have yet to be considered.</p></abstract>

Throughout history, recreational mathematics has always played a prominent role in advancing research. Following in this tradition, in this paper we extend some recent work with crazy sequential representations of numbers− equations made of sequences of one through nine (or nine through one) that evaluate to a number. All previous work on this type of puzzle has focused only on base ten numbers and whether a solution existed. We generalize this concept and examine how this extends to arbitrary bases, the ranges of possible numbers, the combinatorial challenge of finding the numbers, efficient algorithms, and some interesting patterns across any base. For the analysis, we focus on bases three through ten. Further, we outline several interesting mathematical and algorithmic complexity problems related to this area that have yet to be considered.

Crazy Sequential Representations of Numbers for Small Bases

Recreational Mathematics Magazine

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Crazy Sequential Representations of Numbers for Small Bases"}

Throughout history, recreational mathematics has always played a prominent role in advancing research. Following in this tradition, in this paper we extend...

Crazy Sequential Representations of Numbers for Small Bases

Published Online: Feb 07, 2020

Page range: 33 - 48

DOI: https://doi.org/10.2478/rmm-2019-0007

Keywords
representations, algorithms

© 2019 Tim Wylie, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Crazy Sequential Representations of Numbers for Small Bases

Published Online: Feb 07, 2020

Page range: 33 - 48

DOI: https://doi.org/10.2478/rmm-2019-0007

Keywordsrepresentations, algorithms

© 2019 Tim Wylie, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
representations, algorithms