number stairs?

Question

im doing a project on number stairs what things should i be noticing when the stairs is moving on the grid and how do i go about finding the final formular for any size stair on any size grid? ty

Answer 1

A number stair is a step shape on a set grid numbered in sequence.
http://www.subtangent.com/maths/ig-numberstairs.php

So, let's assume the grid is always square, and the starting grid is always 1.... so the number of boxes is always x^2, which is also the largest number contained in the squares.

x = the width of the grid
a = the starting location
s = number of step

So take a simple example shown in the picture in the link above...
a 10 x 10 grid with a 3 step stair give you the following:

x = 10
a = 25
s = 3
r = row number

row 1 sum = (a + 0x + 0) + (a + 0x + 1) + (a + 0x + 2)
row 2 sum = (a + 1x + 0) + (a + 1x + 1)
row 3 sum = (a + 2x + 0)

You can see a pattern emerge... note the last number in each ( ) represent the actual number within the grid.
The second number in each ( ) is the product of x and (s-r)
The last number in each ( ) is ranges from (s-r to 0).

The equation, thus, would require writing summations, which I can't really type out easily in plain text... It should be pretty straight forward from this point on, I will leave it up to you to write it out.

Answer 2

This sounds quite interesting, but I am afraid I do not know enough (or have enough details) to say anything helpful.

Hopefully you wil get some responses from people knowledgable about this specific topic, but if not, perhaps you could post some more details about number stairs.

Good luck!