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### Best Answer Ashok Goyal says

calculus-geomatry:

Is there any formula, permutation and combination. Anyhow without applying any formula I could see only 4+5+2 + 4 + 3 = 18 hexagons.

Where is the +2 ? I got 4 large equilateral hexagons + 5 elongated mini-hexagons + 1 acute mini-hexagon in the center + 4 internal, "parallelohexagons" + 2 (oooooh! nevermind!) mini-equilaterals + ?? + ?? for a total of 16....

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### Courtney Morgan says

I see twenty-two.

Four regular hexagons making up the outer edges.

Four more irregular hexagons in the same spaces not including the overlap.

4+4=8

Two more grayish polygons in the center.

8+2=10

One purple hour-glass shape.

10+1=11

Five oblong hexagons caused by the overlaps.

11+5=16

Subtract the grayish regular hexagons from the four outer oblong hexagons, and you have four bookmark-shaped hexagons.

16+4=20

In the very center, you have two more bookmark-shaped hexagons if you combine the hour glass with the grayish hexagons.

20+2=22

The second set of 4 you mentioned aren't hexagons because they have more than 6 sides.

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### Sid Kemp says

I see 18 at first shot, but that's because I've been playing this game with Calculus-Geometry for too long! :)

Yikes, I missed the 2 horizontal arrows! Revision, thus: 4+5+4+2+2+1=18