7
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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).
    enter image description here
  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

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Second Puzzle

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6
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First puzzle:

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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.

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Second puzzle:

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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:

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