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Exploring Wild & Wonderful Number Patterns
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Dice and Spinner Numbers
If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?
Stage: 2 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
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, that you for this solution.
NRICH is part of the family of activities in the Millennium Mathematics Project.