Copyright © University of Cambridge. All rights reserved.

## 'Beads' printed from http://nrich.maths.org/

V. Rolfe sent the following very clear
solution to the Beads problem:

1) All three beads are red - RRR

When more beads are added, they will also be red as all the beads
are the same colour. The pattern therefore remains the same.

2) Three blue beads - BBB

Three red beads are added as the beads are all the same colour, we
then have the scenario described above, with three red beads and
the pattern remains red.

Thus BBB becomes RRR

3) Two blue beads and one red bead - BBR (The order is not
significant in the circle)

There are two sets of beads of different colours next to each other
therefore two blue beads are inserted. The two blue beads lead to
the insertion of one red bead.

Thus two blue beads and one red bead are added so the pattern
remains constant, although the ring does 'rotate'.

4) Two red beads and one blue bead - RRB

This is the scenario above with two different coloured beads next
to each other and one pair of the same colour. Two blue beads and
one red bead are therefore inserted. When the original beads are
removed the pattern becomes that described above, BBR.

Thank you - you have gone through the
possibilities very systematically.