This activity investigates how you might make squares and pentominoes from Polydron.
If you had 36 cubes, what different cuboids could you make?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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
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
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
eg. A+B and B+A
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!