6. A checker can move in one direction along a strip divided into cells, moving either to the adjacent cell or skipping one cell in a single move. In how many ways can it move 10 cells? 11 cells?
6. Solution. A checker can move to one cell in one way, to two cells in two ways, to three cells $1+2=3$ ways, to four cells $2+3=5$ ways, and so on. It can move to the tenth cell in 89 different ways, and to the 11th cell in 144 different ways. (VZMSh)