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The number within the five triangles of the star is equal to the sum of the three numbers in its surrounding circles.  The number in the center of the star is equal to the sum of the five numbers in its surrounding circles. The numbers in the circles can only be 0 to 9 and each number can be used only once.  Three numbers have been provided to get you started.  Find the remaining seven numbers. [donotprint]

### Solution ### Solution explanation Comments on solving the puzzle; a process of eliminating possible values as answers:

Values 2, 4, 6 are provided and can not be reused.

Starting at Equations (1a & 1b), unknowns F & G are equal to 1 or 5 respectively as shown.

Equation (2): unknowns D & E can only be equal to 0 or 8 as shown. All other combinations include either a 1, 2, 4, 5 or 6 value.

Equation (3): unknowns A, C & D can be equal to 7, 8 or 9 only as shown. Comparing with Equation (2), D can only be equal to 8 and then E is equal to 0. A & C are then equal to 7 or 9 as shown.

Equation (4): unknowns B & C can be equal to 3 or 9 as shown. Comparing with Equation (3), C can only be equal 9 and A is equal to 7 and B is then equal to 3.

Equation (5): 9 + 8 + 6 + 4 + 2 = 29 and thus verifies the center sum of 29.

Now insert your final answers into the original puzzle and verify the resulting sums.

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