Solution

26438

First name
Tim Mallard
School
The Kimberley School 6th Form
Country
Age
18

The numbers I picked were 3 and 7.

3 + 7 = 10

This sum can be visualised as seen in PICTURE 1.

This is 'splitting' the 7 blocks into columns of 3 and adding on the 'extra' or remainder.

From this picture we can deduce the total amount of blocks to be height x length + remainder.

General approach...

f + s = ANSWER where f and s are odd, f<=s

s can be written as a multiple of f (Splitting s blocks into columns of f)

s = kf + r where 0<=r<f, k is an integer.

This means that there are k lots of f in s with r 'left over'.

(Refer to PICTURE 2)

Number of columns = k + 1
Number of rows= f
Number of 'extra'= r

Finally,

f + s = f(k+1)+ r
In my example, f=3, s=7, k=2, r=1

3 + 7 = 3(2+1)+1
= 10.