u-can-do

SQUARE-Sum Walkthrough

by G R Burgin

The Puzzle

The number, in each square, represents the sum of the numbers in the 4 surrounding circles.  The numbers in the circles can only be 1 to 9 and each number can be used only once.  Three numbers have been provided to get you started.  Find the remaining 6 numbers.

The Solution

Comments on Solving Puzzle – a process of eliminating possible values as answers:

Values 3, 4 & 7 are provided and can not be reused.

Starting at Equation (1), unknowns B & D can only be equal to 6 or 9 as shown. All other combinations include either a 3, 4 or 7 value.

Equation (2): unknowns D, F & E can only be equal to 1, 8 or 9 as shown since values 3, 4 & 7 can not be reused. Therefore comparing with Equation (1), D can only be equal to 9 and E & F can be equal to 1 or 8.  Comparing with Equation (1),  B is then equal to 6.

Equation (3): unknowns C & E can be equal 5 or 8 as shown. Comparing with Equation (2), E can only be equal to 8 & C is then equal to 5.

Equation (4): unknowns A, B & C can only be equal to 2, 5 or 6 as shown. Therefore comparing with Equation (1), (2) & (3) with B equal to 6,  C is then equal to 5 and A is equal to 2.

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

Contact: mathspuzzles@gordonburgin.com

© G R Burgin 2009