First, Find out the rule from the example,
Then solve the puzzle without computer. The answer must be unique (just 1 valid answer).
Is this it? (Think this is the unique answer)
The rule is
Each set of three (.-. - Two circles at the bottom one at the top inbetween) circles sums to the number at the bottom, and the red dot indicates that two numbers touching it are 1 apart. And obviously only numbers 1-10 are used.
So we have (bold indicates red dot)
5+4+7=16 and 5-4=1
1+7+8=16 and 8-7=1
9+4+3=16 and 4-3=1
3+7+6=16 and 7-6=1
How I solved this:
There are only two possible set of numbers for the two under 10: 4 and 2 or 5 and 1. First I tried out 4 and 2, found it didn't work, and then tried 5 and 1. I quickly found that the numbers worked. From there it was just trial and error.