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Crossed Ends

Stage: 3 Challenge Level: Challenge Level:1

These crosses can be drawn on number grids of various sizes.

Add opposite pairs of orange numbers (i.e. north + south, east + west).
Notice anything? Try a few more.

Now try the same questions on crosses with two lines of symmetry, like these:

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 other?
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?