Review question

# How many rows can we make with these black and white pebbles? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9664

## Suggestion

Suppose you have an unlimited supply of black and white pebbles. There are four ways in which you can put two of them in a row: $BB$, $BW$, $WB$ and $WW$.

1. Show that for $N \ge 4$ we have $r_N = r_{N-1} + r_{N-2}$. Hint: consider separately the case where the last pebble is white, and the case where it is black.

Using the hint: if the last pebble is white, what do we know about the rest of the row?

1. For $N \ge 5$, write down a formula for $w_N$ in terms of the numbers $r_i$, and explain why it is correct.

What do we know if the first pebble is white? If it’s black?