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Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Mind Reading

Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I know?

How Many Miles to Go?

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

Crossed Ends

Age 11 to 14 Challenge Level:

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 adding opposite pairs on crosses with just two lines of symmetry, like these:

Experiment with grids of various sizes. What do you notice? Can you explain your findings?
You may find these printable sheets useful:
Number Grids - width 3, 4, 5 and 6 
Number Grids - width 7 and 8 
Number Grids - width 9 and 10

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 your findings?