two digadds making 200

place any four digits in the cells (there can be repeated digits)

• read the two 2-digit numbers across and add them
• read the two 2-digit numbers down and add them
• then add these two totals together

you are trying to get a target of 200

students might try to obtain 100 by adding across and 100 by adding 'down'

e.g. with

3 6

 6 4 

having found several solutions, probably by adjusting solutions that are close to 200,

they might notice that the four digits in all of the (several) solutions sum to 19

they can go on to explore this algebraically:

a b

c d

20a + 11(b + c) + 2d = 200

when a = 8,  (b + c)  can only be 2 and d = 9

when a = 7,  (b + c)  can only be 4 and d = 8

and so on...

you can deduce that d - a = 1  if  a + b + c + d = 19

and that 2a +(b + c) = 18