harder magic squares

this work explores how squares can be produced from just 3 given numbers, that are not in a line

note that no other relationships are to be used in developing this work (e.g. the line total being 3 x middle number and the leading diagonal going up in a linear sequence are not to be used)

 students might need help in appreciating that when a column and a diagonal line have a common 'intersection' then the other pairs of numbers must have the same total

once a line of 3 has been found the square is usually easy to complete

find two reasons why the bottom right number must be 4 then complete the remainder...

students could go on to explore what happens when 3 (different) numbers are placed anywhere on the grid (but not in a line)...