Another Correct Order ****

You need to place the numbers in the correct order according to the clues given.  For each problem the numbers may not be in the place that relates to their value.  For example, 1 cannot be in the first position, 2 cannot be in the second place, 3 cannot be in the third place…and so on.

a) Using 1  2  3  and  4:

• The first two digits add to 6.

 b) Using 1  2  3  4  and  5:

• 2 and 3 are at the ends.
• The odd numbers are together.
• The second and fourth cards add to 9.

 Helpful tip:  Write the numbers on little pieces of paper so that you can move them around easily as you try out your ideas.

Find the Values Solution

20 + 9 = 29
18 + 15 + 5 = 38
10 + 11 + 1 = 22

To begin finding the solution, it was helpful to note that each sum needed to have an even number in it.  Can you see why?

Find the Values ****

Using the numbers given, complete the number sentences below.  You may only use each value once.

1   5   9   10   11   15   18   20

____ + ____ = 29

____ + ____ + ____= 38

____ + ____ + ____ = 22

Profit Margin ***

It costs £144 a day to run the dodgems, accounting for wages, electricity, transport, and other costs.  There are 12 dodgem cars and on average 60% of them are occupied each session.  The ride is open for eight hours a day, with four sessions an hour, and the fare is £2 per session.  How much profit is the owner making?

Shaking Hands ****

A group of three friends meet and everyone shakes hands with everyone else once.  How many handshakes are there in total?

Try drawing them out with a dot for each person and lines between them for handshakes.  Now work out the handshakes for groups of four, five or six people.  Can you spot a pattern?

Prison Breakout Solution

As you worked through the puzzle you may have noticed a pattern in the numbers on the doors left open - they are all square numbers.  So the answer is 7 doors:  1, 4, 9, 16, 25, 36 and 49.