Arrange numbers to the triangles, so the sums are equal to S

Question

Rules:

1. Arrange numbers from 1 to 11, and each number can appear max twice.
2. The numbers are arranged, so that any 3 numbers which forming an up-triangle sum to the desired number (S).
   
3. A equal sign means one rectangle's number is the same number of another one.
4. A line sign means one rectangle's number is adjacent to another one.
5. The puzzle can be solved without computer.
6. Explain your way to solve the puzzle.

First Puzzle

Second Puzzle

Answer 1

First puzzle:

By the link with the 4, the blues must be either threes or fives. If they are threes, then the reds are 10 and 11, and the up-triangle containing both reds has a sum that is too large. Therefore the blues are 5. The first green circle is then a 3, because both fives are taken. For the other two, their sum must be 7, so they can only be 3 and 4. Filling in the rest of the yellow circles, we can see that the rightmost circle in the bottom row must be an 8, for if it were a 6 we would need to use an extra 4.

Second puzzle:

Blues are obviously 7. Now the leftmost yellow and the red circles must be 6 and 6, or 8 and 4. If they are both sixes, then the fact that the yellows are the same as the oranges leads to a contradiction, as we can't use any more sixes. So red is 4, and yellows must be 8 and 9 (because 7 is already taken), oranges also being 8 and 9. This allows us to fill all green squares. Then the topmost circle is either 6 or 4; but if it is 6 then we need an extra 8 which we can't use, so it must be 4. The rest can be then filled out: