This problem is the most interesting because everyone who sent in a solution explained it a bit differently. Look at all the patterns they found!
Abubakr, Noor, Faiza, Krishan and Catherine (Bancrofts Prep, Woodford Green) started by giving each child a number from 1 to 7. They said:
We paired child 1 to each of the others, and then child 2 to each of the other (except 1) and so on.
These are the 21 pairs they made, giving the answer of 21 rides.
1 1 1 1 1 1 2 3 4 5 6 7 2 2 2 2 2 3 4 5 6 7 3 3 3 3 4 5 6 7 4 4 4 5 6 7 5 5 6 7 6 7
Syed (Foxford School and Community College) used a letter for each child. He says:
1. First I give a name to call each friend:
A, B, C, D, E, F, G
2. Then I write the rides that each friend is going to have:
A+B B+A C+A D+A E+A F+A G+A
A+C B+C C+B D+B E+B F+B G+B
A+D B+D C+D D+C E+C F+C G+C
A+E B+E C+E D+E E+D F+D G+D
A+F B+F C+F D+F E+F F+E G+E
A+G B+G C+G D+G E+G F+G G+F
3. Then I cross out one of every two rides that are identical
eg. A+B and B+A
B+A C+A D+A E+A F+A G+A
C+B D+B E+B F+B G+B
A+D B+D C+D
D+C E+C F+C G+C
A+E B+E C+E D+E
E+D F+D G+D
A+F B+F C+F D+F E+F
A+G B+G C+G D+G E+G F+G
4. Then I count all the rides that are not crossed out.
6 + 5 + 4 + 3 + 2 + 1 + 0 = 21
The answer is 21.
Rebecca, Rachel, Louise, Charlotte and Elizabeth (Burpham Primary, Guildford) discovered this adding pattern at the end too. Rachel and Louise said:
We found that you can add all the numbers below 7 to get the answer.
Danielle and Elizabeth (Stamform High) took their thinking a bit further ...
The quick way to do this would be 7x7=49 or whatever number of people x the same number - that number divided by 2.
So if there were 70 people it would be 70 x 70 = 4900 - 70 =
4830 divided by 2 = 2415 rides to go on.
Phew! If it cost a pound a ride you would be broke!