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[jasen]

Put numbers 1,2,3,4,5,6,8,9,10,12 each point, so :
- The sum of points in every line  are equal,
- A+B+C+D+E = D+E+F+G+H

There are 2 solutions.  
(Rotation and Reflection are considered as 1 same solution)

[Logophobic]

Spoiler

 

[jasen]

 

9 hours ago, Logophobic said:

 

Very good start, your second answer is right, 
but the first answer is wrong, because 1+6+9+5+12 =/= 10+4+2+8+3.

We can easily find the other right answer from the first right answer.
use your second answer to find another right answer (ofcourse without rotation and reflection)
hint : put the inner points to the outer points.

 

Edited February 17, 2016 by jasen

[Logophobic]

1+6+9+5+12 = 5+12+10+4+2, as required: A+B+C+D+E = D+E+F+G+H

Of course, A+B+C+D+E = F+G+H+I+J does seem more appropriate, but I was working with what you posted.

[jasen]

13 hours ago, Logophobic said:

1+6+9+5+12 = 5+12+10+4+2, as required: A+B+C+D+E = D+E+F+G+H

Of course, A+B+C+D+E = F+G+H+I+J does seem more appropriate, but I was working with what you posted.

Ok, I just realize my question was wrong, yes it should be A+B+C+D+E = F+G+H+I+J