Team Scream
Seven friends went to a fun fair with lots of scary rides.
They decided to pair up for rides and keep swapping partners until each friend had ridden once with each of the others.
What was the total number of rides taken by them all?
How will you keep track of what you have done?
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
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
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!