Question

#9: is the 16th figure black or white? 1 point white #10: is the 19th figure black or white? 1 point white #11: what is the shape of the 10th figure? 1 point circle #12: what is the shape of the 18th figure? 1 point

Explanation:

Step1: Identify the pattern of colors

The pattern of colors (white - black - white - black - white - black) repeats with a period of 2.

Step2: Determine the color of the 16th figure

Divide 16 by 2: $16\div2 = 8$ with no remainder. Since the remainder is 0, following the pattern, the 16th figure has the same color as the 2nd figure in the repeating unit, which is black.

Step3: Determine the color of the 19th figure

Divide 19 by 2: $19 = 2\times9+1$. The remainder is 1. So the 19th figure has the same color as the 1st figure in the repeating unit, which is white.

Step4: Identify the pattern of shapes

The pattern of shapes (circle - square - hexagon) repeats with a period of 3.

Step5: Determine the shape of the 10th figure

Divide 10 by 3: $10 = 3\times3 + 1$. The remainder is 1. So the 10th figure has the same shape as the 1st figure in the repeating unit, which is a circle.

Step6: Determine the shape of the 18th figure

Divide 18 by 3: $18\div3=6$ with no remainder. So the 18th figure has the same shape as the 3rd figure in the repeating unit, which is a hexagon.

Answer:

#9: black
#10: white
#11: circle
#12: hexagon