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Sum Thing

Be aware that not all puzzles necessarily use all numbers in the given range.

Write a distinct number in every circle, such that the numbers in circles bordering an area with a number, sum up to that number. Next to the puzzle the range of allowed numbers is given.

Example

The puzzle on the left uses the numbers 1 through 5. These sum up to 15, which means that the two circles not bordering the region with 11 in it, have to sum up to 4 and are therefore supposed to be 1 and 3. The 3 can not be in the circle bordering the region with 7, because the only way to write 7 as the sum of three distinct positive numbers is 1+2+4. So we can put the 1 at the top and the 3 at the bottom. The 7 can only be completed with the 2 and the 4. The 10 can only be completed with the 2 and the 5. Since they need to share the 2, it is now clear where each number goes.


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