Congratulations to the many people who sent in excellent solutions. Jeni and Lucy , St James Middle School, Bury St Edmunds and Jackie of Madras College, St Andrews used trial and improvement. All the following used algebra: Timothy of Munsang College, Hong Kong; Kate and Katherine of Emmbrook School, Wokingham; Lyndsey, Christiane and Joanne ofThe Mount School, York; Fiona and Elizabeth of Stamford High School, Lincs.

Here is the solution from Prav, Sheli, Meg, Ruoyi & Liz The North London Collegiate School Puzzle Club.

Dear Cambridge,

We have a solution to the Rollerball question published in the May problems. We made a formula to find out the prize money which we called £x.


100 + 1
10
 (x - 100)
=
200 + 1
10
 [ ( x - 300 ) - 1
10
 (x - 100) ]
100 + x
10
 - 10
=
200 + 1
10
 (x - 300 - x
10
 + 10)
x
10
 + 90
=
200 + 1
10
 ( -290 + 9x
10
 )
x
10
 + 90
=
200 - 29 + 9x
100
x
10
 + 90
=
171 + 9x
100
x
10
=
81 + 9x
100
x
100
=
81
x
=
8100

The first child gets:


100 + 1
10
 (8100 - 100) = 900.

Therefore, if every child gets the same amount, so
£8100
£900
 = 9

there are nine children.

Love from, Prav, Sheli, Meg, Ruoyi & Liz