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AMO 2027 Grades 6-7 SET 20 - Self-study Question 5

AMO · AMO 2027 Grades 6-7 SET 20 - Self-study

Question 5

The pictures below are made up of squares and 6-sided shapes, each of which is added one shape at a time. Figure 1 has 17 lines, figure 2 has 20 lines and figure 3 has 25 lines. How many lines will there be in figure 8?

**Editorial note for this self-study exercise:** Continue alternating squares and hexagons to the right, each new shape sharing exactly one whole side with the preceding shape. Count each drawn side once, including shared internal sides. Enter the number of lines.

Question illustration