I am making a bracelet using beads, with colours red, yellow, green and white. My bracelet satisfies the following properties:
a) All pairs of red beads have two beads between them.
b) All pairs of yellow beads have three beads between them.
c) All pairs of green beads have four beads between them.
d) The first three beads are all different colours, but none is white.
What is the maximum number of beads I could have in my bracelet?