An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Find a great variety of ways of asking questions which make 8.
Choose any three by three square of dates on a calendar page.
Circle any number on the top row, put a line through the other
numbers that are in the same row and column as your circled number.
Repeat this for a number of your choice from the second row. You
should now have just one number left on the bottom row, circle it.
Find the total for the three numbers circled. Compare this total
with the number in the centre of the square. What do you find? Can
you explain why this happens?
Is it possible to rearrange the
numbers 1, 2 ...12 around a clock face in such a way that every two
numbers in adjacent positions differ by any of 3, 4 or 5 hours?
How many solutions can you find?
Can you convince us that you have all of them?