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'Crossed Ends' printed from http://nrich.maths.org/
These crosses can be drawn on number grids of various sizes.
Add opposite pairs of orange numbers (i.e. north + south, east +
Notice anything? Try a few more.
Now try the same questions on crosses with two lines of symmetry,
Experiment with grids of various sizes until you know that it's a
coincidence, or until you know why it must always work. A sheet of
number grids is available here
What happens if you add the orange squares in adjacent pairs? (try
N + W, S + E )
Can you predict in advance how the totals will relate to each
What does it depend on?
Is it the same if you added them the other way round? (i.e. N + E,
S + W)
Can you explain what you are finding?