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Answer: There are 64 hexagon-type shapes in total.

There are 37 single hexagons, 19 hexagons which contain 7 smaller hexagons, 7 hexagons which contain 19 smaller hexagons and one large hexagon which contains all of the smaller hexagons.

Puzzle 2

Add lines to this grid and create five areas that each have 4 letters, to spell five 4-letter words.

Hint: The lowest route contains more 2's than the highest route.

Answer: Highest = 24. Lowest = 12.

Puzzle 4

Last week I travelled from London to Leeds, which is a distance of 174 miles.

I started at 9.15am and completed the journey with an average speed of 40 miles per hour.

On the way back, in the evening, I travelled exactly the same route, starting at 5.15pm. The traffic was light and I completed the journey with an average speed of 60 miles per hour.

What was the overall average speed for round trip?

Hint: Remember that Time = Distance ÷ Speed, and Speed = Distance ÷ Time.

Answer: 48 miles per hour.

Time = Distance ÷ Speed
Speed = Distance ÷ Time

The outward journey took 174 miles ÷ 40 mph = 4.35 hours.

The return journey took 174 miles ÷ 60 mph = 2.9 hours.

So I travelled a total of 2 x 174 = 348 miles. I did this in a total of 4.35 + 2.9 = 7.25 hours.

My overall average speed was therefore 348 miles ÷ 7.25 hours = 48 miles per hour. QED.

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