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Triangles 60 Diamonds 60 Hexagons 10

Triangles

Count the triangles by size.

Shape	Method 1	Method 2	Method 3	Count
	(1 + 3 + 5 + 7) × 2	(4 + 4 + 4 + 4) × 2	4² × 2	32
	(1 + 2 + 3 + 2 + 1) × 2	(3 + 3 + 3) × 2	3² × 2	18
	(1 + 2 + 1) × 2	(2 + 2) × 2	2² × 2	8
	1 × 2	—	1² × 2	2

Total

32 + 18 + 8 + 2 = 60

Diamonds

Count the diamonds by size.

Shape	Formula	Breakdown	Count
	4 × 4	16	40
	3 × 4 × 2	24
	3 × 3	9	15
	3 × 2	6
	2 × 2	4	4
	1	1	1

Total

40 + 15 + 4 + 1 = 60

Hexagons

Count the hexagons by size.

Shape	Method 1	Method 2	Count
	1 + 2 + 3 + 2 + 1	3²	9
	1	1²	1

Total

9 + 1 = 10

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