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Many of you approached this problem in the same way to start with. Maddie and Alex from The Mount School wrote:
We found out that 1+2+3+4+5+6...+20=210. Because we needed 7 different subsets that when added together made 7 consecutive numbers, we divided 210 by 7. 210/7=30Thank you, Boris. Many of you suggested ways to make pairs of numbers and then add a third to total one of the consecutive numbers like Boris' method.
Ivo from Gresham's Prep School used a different method to work out which consecutive numbers to aim to make:
Thank you, Ivo! Zoe, Andrew, Nikita and Ben from Aqueduct Primary School went about the problem in a slightly different way:
A | B | C | Answer |
2 | 7 | 16 | 25 |
4 | 5 | 17 | 26 |
0 | 1 | 2 | 3 | 4 | 5 | 6 |
7 | 8 | 9 | 10 | 11 | 12 | 13 |
14 | 15 | 16 | 17 | 18 | 19 | 20 |
A | B | C | Answer |
0 | 7 | 14 | 21 |
1 | 8 | 15 | 24 |
2 | 9 | 16 | 27 |
3 | 10 | 17 | 30 |
4 | 11 | 18 | 33 |
5 | 12 | 19 | 36 |
6 | 13 | 20 | 39 |
A | B | C | Answer |
0 | 13 | 14 | 27 |
1 | 12 | 15 | 28 |
2 | 11 | 16 | 29 |
3 | 10 | 17 | 30 |
4 | 9 | 18 | 31 |
5 | 8 | 19 | 32 |
6 | 7 | 20 | 33 |
Thank you Zoe, Andrew, Nikita and Ben. It is always good to receive solutions which take us all the way through the process that you followed to solve the problem. Your solution shows us that "playing" with a problem can be a very good way to start and will often lead to us finding something out that helps us go about a solution more systematically (in other words more logically).