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Wallpaper

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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 into smallest 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.

Greg from the USA wrote: 

E, B, A, F, G, C, D

I compared visually each wallpaper piece to another. I found the two smallest and two largest. The middle three were difficult. I imagined the long ones folding in on themselves. It was easier when I noticed the shape edges were similar on pieces A and F.

If I cut them out, I would lay one on top of the other to better compare their sizes. Tracing the outlines might help too.

Hannah, Holly, Paddy from Carriglea NS in Ireland wrote:

We worked it out by looking at the shapes and by counting the full and half stars and dots in the shapes. The order of the shapes is:

E, F, G, B, A, C, D

So we have different answers and different methods.  What do you think about that?