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Adding All Nine

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!

Always the Same

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

Master Minding

Age 11 to 14
Challenge Level

Picture of beads on either side of screen - as if partner is guessing the choice and position of the beadsYou have any number of beads of three different colours (red, yellow and blue).

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?

  • For each bead you choose of the right colour but put it in the wrong place you get one point
  • For each bead you choose of the right colour that you put in the right position you get two points.
  • Your partner tells you the total number of points.

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?)