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

First of all we have Izzy's examples:-

 9 2 by 2 2 4 by 4 32 1 by 1 43 Total  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:-

 2 5 by 5 1 3 by 3 1 4 by 4 4 2 by 2 9 1 by 1 17 Total  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:-

 20 2 by 2 20 1 by 1 40 Total  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.

 14 2 by 2 2 3 by 3 26 1 by 1 42 Total  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.