There are 3 numbers in the middle. I started by assuming that the biggest 3 were going to be in the middle
I draw the triangle with circles where the 15 numbers would be. Since the smallest sum was required I put 1,2, and 3 in the corners.
then I added one number to each side stating at 4 and working upwards. Each time I was careful to keep the sum of the sides as close in value as possible. So I added 4,5and 6 (checked the sum) then 7,8,and 9 (checked the sum) and lastly 10, 11 and 12 (checked the sum).
It all fell out rather nicely. I don't need to give you the answer. Have a play yourself.
+118654 
