2020 AMC 8
Complete problem set with solutions and individual problem pages
Three hexagons of increasing size are shown below. Suppose the dot pattern continues so that each successive hexagon contains one more band of dots. How many dots are in the next hexagon?
- A.
- B.
- C.
- D.
- E.
Solution 1
Looking at the rows of each hexagon, we see that the first hexagon has dot, the second has dots, and the third has dots. Given the way the hexagons are constructed, it is clear that this pattern continues. Hence, the fourth hexagon has dots.
Solution 2
The dots in the next hexagon have four bands. From innermost to outermost:
. The first band has dot.
. The second band has dots: dot at each vertex of the hexagon.
. The third band has dots: dot at each vertex of the hexagon and other dot on each edge of the hexagon.
. The fourth band has dots: dot at each vertex of the hexagon and other dots on each edge of the hexagon.
Together, the answer is
