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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

Starting with any number on the top row, make your way to the bottom, adding the numbers as you go.

Each time you go to the next row, you can move straight down, or one place to the left or right.

What is the highest total you can make? What is the lowest?

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

Answer: Highest = 24. Lowest = 12.

Puzzle 3

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.

Puzzle 4

You are given a 10x10x10 cube composed of one thousand 1x1x1 mini-cubes glued together.

If you removed the outermost layer, how many mini-cubes would you have removed?

[Ref: ZVPY]

Hint: Think about one face at a time.

Answer: 488.

You started with 10x10x10 = 1000 cubes.

Removing the outermost layer would leave a 8x8x8 large cube = 512 cubes.

Therefore you would have removed 488 cubes (1000 - 512 = 488).

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