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Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

The Deca Tree

Age 7 to 11
Challenge Level

This problem was very well answered. We had many very well explained solutions but Kirsty's solution was particularly clear:

There are 10 leaves per twig
There are 10 twigs per branch
10 leaves x 10 twigs = 100 leaves per branch
There are 10 branches per trunk
100 leaves x 10 branches = 1000 leaves per trunk
There are 10 trunks per tree
1000 leaves x 10 trunks = 10 000 leaves on the tree

Cut off one trunk: 10 000 - 1000 = 9000 leaves left
Cut off one branch: 9000 - 100 = 8900 leaves left
Cut off one twig: 8900 - 10 = 8890 leaves left
Pull off one leaf: 8890 - 1 = 8889 leaves left

There are 8889 leaves left on the tree.

This is excellently explained, Kirsty - you have approached the problem very systematically.
Rachel who goes to Aldermaston CE Primary School also sent in a fantastic solution. She did it in the same way as Kirsty, but found the total number of leaves which had been pulled off before the total number of leaves on the tree to start with.

Here is everyone else who sent extremely clear solutions which were similar to either Kirsty's or Rachel's. You all deserve a mention - thank you!

Alistair from Histon and Impington Junior School
Benjamin, Becki, Pauline, Chris, Elliot, Luke, Ryo and Jake from Moorfield Junior School
Bianca and Kathryn from Devonshire Primary School
Goh Bee, Khoo Kian, Tan Yan, Tan Jun, Tao Mai and Ng Hui at Corporation Primary School in Singapore
Hannah from South Parade Junior School
Jennie at St. Nicolas CE Junior School, Newbury
Jonathan at Dobcroft Junior School, Sheffield
Joshua from Hillside Community Primary School, Ipswich
Rachael from Ardingly College
Stephen from Moorlands School
Adam and Toby from Chacombe CE Primary School
Chad who goes to the Canadian Academy
Rushad, Oliver and Sabrina from Tanglin Trust School, Singapore
Douglas from Burgoyne Middle School
Vinny from Our Lady of the Assumption in Blackpool.

We have also had this solution sent in by Riana, Leah, Charlie and Oliver from St. James' Academy in Bournmouth, using the mathematical term "powers" to indicate a number multiplied by itself a number of times.

First we did 10 to the power of 4 because there are 10 trunks, 10 branches, 10 twigs and 10 leaves. The answer we found from that was 10,000.
There are 1000 leaves on one trunk, 100 leaves on a branch, 10 leaves on a twig and 1 leaf left. This all totalled 1111. We then took this from 10,000 which left us with the answer, 8889 leaves left over!

Well done, thank you for this solution.