1040 grid, 3 boxed, what space?

Question

A grid

I have a grid with boxes. The total grid is 1040 wide.

Number of boxes and spaces

I have 3 boxes an 2 spaces between them.

Question

What are the number of pixels between the boxes, the spaces? I want to come as close to space number 15 as possible. The problem I have is that the sum is never exact 1040.

The space don't have to be 15 but every box needs to be equal in width.

|Box1|Space|Box2|Space|Box3|

I tried to set the space to 15 but ( 1040 - ( 15 x 2 ) ) / 3 = 336,667

I want the box to be a whole number like 336. The number of 15 can change close to it up or down.

Answer 1

If $b$ is the width of a box and $s$ the width of the space between them, then your requirements can be expressed as follows:

$$ 3b + 2s = 1040 \Rightarrow s = {{1040-3b}\over{2}} = 520 - {3 \over 2} b $$

To make $s$ an integer requires that ${3 \over 2 } b$ be an integer. Thus, $b = 2k$, for $k=1,2,\dots$, and the possible values of $s$ and $b$ will be

$$\begin{array}{rcl} b & = & 2k \\ s & = & 520 - 3k \end{array} $$

for integers $k < 520/3$.

As an example, for $k = 168$, we have that $s=16$ and $b=336$, which gives

$$ 3 \cdot 336 + 2 \cdot 16 = 1040. $$