Copyright © University of Cambridge. All rights reserved.

## 'Master Minding' printed from http://nrich.maths.org/

You 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?)