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My New Patio

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

Tiles on a Patio

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

These solutions are just some examples showing the work of four children.

First of all we have Izzy's examples:-

Tiling pattern
9  2 by 2
 

 

 

 
 2  4 by 4
 

 

 

 
32  1 by 1
 

 

 

 
43  Total

Tiling pattern
96  1 by 1
 

 

 

 
 1  2 by 2
 

 

 

 
97  Total

Izzy found that you could not get a solution using 98 or 99 tiles so the next highest after 100 was this one with just 1 2 by 2 replacing 4 1 by 1's.

Now we see Lizzy's:-

Tiling pattern
2  5 by 5
 

 

 

 
 1  3 by 3
 

 

 

 
 1  4 by 4
 

 

 

 
 4  2 by 2
 

 

 

 
 9  1 by 1
 

 

 

 
17  Total

Tiling pattern
16  2 by 2
 

 

 

 
20  1 by 1
 

 

 

 
 1  4 by 4
 

 

 

 
37  Total

I rather liked her 17 made up of 5 different sizes. The 37 was not symmetrical, many results were, that's neither good nor bad ... it's all O.K.

Then we have Ben:-

Tiling pattern
20  2 by 2
 

 

 

 
20  1 by 1
 

 

 

 
40  Total

Tiling pattern
8  2 by 2
 

 

 

 
 1  6 by 6
 

 

 

 
32  1 by 1
 

 

 

 
41  Total

His 41 would really look good if you wanted it to be very symmetrical. You could probably invent some games in going around the edge from 4 1 by 1's to a 2 by 2. The 40 is interesting because there is the same number of each tile size.

Tiling pattern
14  2 by 2
 

 

 

 
 2  3 by 3
 

 

 

 
26  1 by 1
 

 

 

 
42  Total

Tiling pattern
12  2 by 2
 

 

 

 
 1  3 by 3
 

 

 

 
 1  5 by 5
 

 

 

 
18  1 by 1
 

 

 

 
32  Total

I think Bo's 42 is rather like a robot! The 32 was very different.

Well done and thank you Izzy, Lizzy, Ben and Bo. Yes these are four real children from the South West of England who were in a group of 19 doing this activity.