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## 'Wallpaper' printed from http://nrich.maths.org/

This problem was well answered - thank you to
all who sent us solutions. Most of you explained that you worked
out the size of each piece of wallpaper by counting the number of
stars and spots. Jamie from Great Sankey High School decided to
show this in a table. He said:

First, I found out how many stars and circles there were in each
irregular shape. I then wrote it in a graph

(I think Jamie means a table here) to show
my results clearly. I then added up each of the totals to make a
grand total of shapes for each irregular shape. Finally, I ranked
them smallest first to end up with a solution.

Shape |
Stars |
Circles |
Total |
Place |

A |
13 |
12 |
25 |
5 |

B |
10 |
9 |
19 |
4 |

C |
18 |
17 |
35 |
6 |

D |
19 |
19 |
38 |
7 |

E |
4 |
5 |
9 |
1 |

F |
9 |
7 |
17 |
2 |

G |
9 |
9 |
18 |
3 |

(In fact, Jamie ordered them from largest to
smallest in his solution, but I've changed them intosmallest to
largest in the table so that it matches the question.) So, Jamie
concluded, that from smallest to largest the shapes were: E, F, G,
B, A, C, D.

Rowena from Christ Church Infants also
recorded her results in a table - a good idea. Some of you didn't
agree exactly with Jamie's final order, but it depended on how you
counted the stars and spots. Jack from Hitchin Boys' School
said:

I found the solution by counting the amount of circles and
stars in each shape, two halves making one.

It wasn't always easy to decide when a shape
was half and when it was less or more than half was it?