# You're reading: Posts Tagged: sequences

### Sequences in the triangle and the fourth dimension

This is the second in a series of guest posts by David Benjamin, exploring the secrets of Pascal’s Triangle.

## Sequences in the diagonals

There are many sequences of numbers to be found in Pascal’s triangle. The Natural numbers occur in the second diagonal, running in either direction, and the next two diagonals after that contain other important sequences:

## Sequences in the diagonals

There are many sequences of numbers to be found in Pascal’s triangle. The Natural numbers occur in the second diagonal, running in either direction, and the next two diagonals after that contain other important sequences:

### Guest post: Sequence Numbers

This is a guest post, sent in by David, who’s discovered an interesting property of numbers, and is looking for collaborators to take it further.

Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere.

– W. S. Anglin

A few years ago I saw a post on a website that showed that the inverse of 998,001 produces a decimal expansion that counts, using three digit strings, from 000 to 997 without error.

$\frac{1}{998,\!001} = 0.0000010020030040050060070080090100110120130\ldots$

I immediately thought that this had to be a hoax. I decided to work it out to prove it was a hoax – after all some people put anything they want on the web whether it is true or not.

### Puzzlebomb – July 2015

Puzzlebomb is a monthly puzzle compendium. Issue 43 of Puzzlebomb, for July 2015, can be found here:

Puzzlebomb – Issue 43 – July 2015

The solutions to Issue 43 can be found here:

Puzzlebomb – Issue 43 – July 2015 – Solutions

Previous issues of Puzzlebomb, and their solutions, can be found here.

### I’ve made my own numbers-in-a-grid game

For the past couple of weeks, I’ve been obsessively playing the game Twenty on my phone. The fact that my wife has consistently been ahead of my high scores has nothing to do with it.

The main source of strife in my marriage.

Twenty is another in the current spate of “numbers-in-a-grid” games that also includes Threes, 10242048 (and its $2^{48}$ clones), Just Get 10, and Quento.

The basic idea is that you have a grid of numbered tiles, and you combine them to build up your score. While there are lots of unimaginative derivatives of the bigger games, there’s a surprisingly large range of different games following this template.

With so many different games being created, I thought that a chap like me should be able to come up with a numbers-in-a-grid game of my own. Yet, for a long time, I just couldn’t come up with anything that was any good.

Yesterday I had a really nice shower, and the accompanying feeling that I’d come up with a really good idea – make a game to do with arithmetic progressions.