Choose any three by three square of dates on a calendar page...
Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some other
possibilities for yourself!
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
You have any number
of beads of three different colours (red, yellow and
Your partner chooses any two beads and places them side by side
on two spikes hidden behind a screen.
If you have to guess the two beads and their positions by
placing two beads, on pairs of pegs, on the table in front of the
screen - what is the minimum number of guesses you would need to be
sure of getting it right?
If, every time you put two beads down, your partner gives you
feedback in the following form. What would be the minumum number of
goes you would now need to be sure of getting it right?
So two points could mean one of your beads is the right colour
and in the right place or the two beads are the right colours but
in the wrong places.
What is the best strategy for getting the correct answer in the
least number of moves? (e.g. should you put two beads of the same
colour first? Then what?)