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The four numbers in italics outside the nine circles represent the sum of the numbers in the five surrounding circles.  The numbers in the circles can only be 1 to 9 and each number can be used only once.  Four numbers have been provided to get you started.  Find the number that should be in the center of the X. ### Solution ### Solution explanation Comments on solving the puzzle; a process of eliminating possible values as answers:

Values 6, 7, 8 & 9 are provided and can not be reused.

Starting at Equation (1), unknowns A, B & ? can only be equal to 1, 2, 3, 4 or 5 as shown. All other combinations can not include either a 6, 7, 8 or 9 value.

Equation (2): unknowns B, C & ? can also be equal to 1, 2, 3, 4 or 5 as shown.

Equation (3): unknowns C, D & ? can only be equal to 1, 2 or 3 as shown. Comparing with Equation (2), values 4 & 5 can be eliminated as possible values for C & ?. As a result, unknown B can still be equal to 4 or 5 as shown.

Equation (4): unknowns D, A & ? can be equal to 1, 2 or 4 as shown. Comparing with Equation (3), value 4 can be eliminated as a possible value for D & ?. As a result, the final answer for A can only be equal to 4, ? equal to 1 & D equal to 2 as shown. Comparing with notes (1) & (2), the final answers for B can only be equal to 5 and C equal to 3.

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

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