The relationship of the figure number to the number of the black beads is figure numberx figure number. So figure 1 has 1x1 black beads, figure 2 has 2x2 black beads, figure 3 has 3x3 black beads and so on. So figure 20 will have??

For the white beads, the relationship to figure number is not as evident. But look at it like that. Look at the white beads for figures 3. Take out the white beads at the 4 corners and you are left with 3 beads on every side. Same with figure 2. So to find out the figure number, take the number given to you, minus 4 and divide by 4