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Magic Triangle

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

Michael and Robert from Necton Middle School in Norfolk sent the following solution, where the sides all add up to 17:


Simone from Stroud Green Primary School sent us another solution where the sides all add up to 17.


Simone's solution

In fact, there are lots more solutions. Here's a list of them (including the two shown above). Each group of four numbers makes up a side of the triangle. Of course, within a side you can switch round numbers that aren't on a corner, but that doesn't really give any new solutions.


17 = 1 + 5 + 9 + 2 = 2 + 4+ 8+ 3 = 3 + 6 + 7 + 1
17 = 1 + 6 + 8 + 2 = 2 + 5 + 7 + 3 = 3 + 4 + 9 + 1

19 = 1 + 5 + 9 + 4 = 4 + 2 + 6 + 7 = 7 + 3 + 8 + 1
19 = 1 + 6 + 8 + 4 = 4 + 3 + 5 + 7 = 7 + 2 + 9 + 1
19 = 2 + 5 + 9 + 3 = 3 + 1 + 8 + 7 = 7 + 4 + 6 + 2
19 = 2 + 6 + 8 + 3 = 3 + 4 + 5 + 7 = 7 + 1 + 9 + 2

20 = 1 + 6 + 8 + 5 = 5 + 2 + 4 + 9 = 9 + 3 + 7 + 1
20 = 2 + 4 + 9 + 5 = 5 + 1 + 6 + 8 = 8 + 3 + 7 + 2
20 = 2 + 6 + 7 + 5 = 5 + 3 + 4 + 8 = 8 + 1 + 9 + 2
20 = 3 + 4 + 8 + 5 = 5 + 2 + 6 + 7 = 7 + 1 + 9 + 3
20 = 4 + 2 + 9 + 5 = 5 + 1 + 8 + 6 = 6 + 3 + 7 + 4
20 = 4 + 3 + 8 + 5 = 5 + 2 + 7 + 6 = 6 + 1 + 9 + 4

21 = 3 + 5 + 7 + 6 = 6 + 2 + 4 + 9 = 9 + 1 + 8 + 3
21 = 3 + 4 + 8 + 6 = 6 + 1 + 5 + 9 = 9 + 2 + 7 + 3
21 = 3 + 2 + 9 + 7 = 7 + 1 + 5 + 8 = 8 + 4 + 6 + 3
21 = 3 + 5 + 6 + 7 = 7 + 2 + 4 + 8 = 8 + 1 + 9 + 3

23 = 7 + 2 + 6 + 8 = 8 + 1 + 5 + 9 = 9 + 3 + 4 + 7
23 = 7 + 3 + 5 + 8 = 8 + 2 + 4 + 9 = 9 + 1 + 6 + 7