Starting in the bottom left corner and moving either up or right, one square at a time, adding up the numbers along the way, what is the largest sum which can be made once you have reached the top right corner?

At the local model boat club, four friends were talking about their boats.

There were a total of eight boats, two in each colour, red, green, blue and yellow. Each friend owned two boats. No friend had two boats of the same colour.

Alan didn't have a yellow boat. Brian didn't have a red boat, but did have a green one. One of the friends had a yellow boat and a blue boat and another friend had a green boat and a blue boat. Charles had a yellow boat. Darren had a blue boat, but didn't have a green one.

Can you work out which friend had which coloured boats?

Answer:
Alan had a red boat and a green boat.
Brian had a green boat and a blue boat.
Charles had a yellow boat and a red boat.
Darren had a blue boat and a yellow boat.

Puzzle 353

A rope swing hangs vertically down so that the end is 12 inches from the ground, and 48 inches from the tree.

If the swing is pulled across so that it touches the tree, it is 20 inches from the ground.

Hint: You might find Pythagoras' theorem very useful [a^{2} + b^{2} = c^{2}].

Answer: 148 inches.

We can use Pythagoras' theorem if we draw an imaginary line across to create a right-angled triangle.

The hypotenuse is equal to the rope's length R. The bottom of the triangle is 48 inches. The vertical side is R - 8 (the difference between 20 inches and 12 inches).

Pythagoras' theorem tells us that:

a^{2} + b^{2} = c^{2}

Where c is the hypotenuse.

This gives us:

48^{2} + (R - 8)^{2} = R^{2}

^{ }^{ } 2304 + (R - 8)(R - 8) = R^{2}

^{ } 2304 + R^{2} - 16R + 64 = R^{2}

^{ }^{ } 2304 - 16R + 64 = 0

^{ }^{ } 16R = 2368

^{ }^{ } R = 148

As required. QED.

Puzzle 354

Hidden in each of the sentences are the numbers 1 to 10 in words.

A number might appear in more than one sentence, but there is only one way to find all ten numbers.

For example 'My parents told me to never cross the road without looking.' contains the number 1: 'My parents told me to never cross the road without looking.'

The robins love hiding amongst the smooth reeds.

It's always worth looking after your friends, even if they've upset you.

Even heavyweight boxers like using soft tissues when they have a cold.

To avoid the calf, I veered sharply to the left.

The eggs were boxed thirteen instead of a dozen in each baker's delivery box.

Having salmon every day for lunch gets a little boring after a while.

The attendance at the local football match exceeded last weeks by many thousands.

We need to waterproof our boots to make sure we don't get wet.

Meeting friends after work allows executives to network effectively.

The orchestra sounded magnificent with the three virtuosi xylophonists.

3 - The robins love hiding amongst the smooth reeds.
7 - It's always worth looking after your friends, even if they've upset you.
8 - Even heavyweight boxers like using soft tissues when they have a cold.
5 - To avoid the calf, I veered sharply to the left.
9 - The eggs were boxed thirteen instead of a dozen in each baker's delivery box.
1 - Having salmon every day for lunch gets a little boring after a while.
10 - The attendance at the local football match exceeded last weeks by many thousands.
4 - We need to waterproof our boots to make sure we don't get wet.
2 - Meeting friends after work allows executives to network effectively.
6 - The orchestra sounded magnificent with the three virtuosi xylophonists.

Puzzle 355

Using the BrainTracker grid below, how many words can you find? Each word must contain the central H and no letter can be used twice. The letters do not have to be connected. Proper nouns are not allowed, however, plurals are. Can you find the nine letter word?