SOLUTION: Each of the numbers 1,2,3,4...12 is to be placed in one of the circles. The sum of the entries along each side of the square equals to 22. determine the sum of the numbers that app

Question 389235: Each of the numbers 1,2,3,4...12 is to be placed in one of the circles. The sum of the entries along each side of the square equals to 22. determine the sum of the numbers that appear in the four corner circles.
Note: I could not draw a picture. there are 12 circles arranged in the form of square shaped figure.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
The sum of all the entries 1, 2, ..., 12 is equal to (12*13)/2 = 78. If we add each side length, as in (x_1 + ...x_4) + (x_4 +... + x_7) + (x_7 + ...+x_10) + (x_10 + ...+ x_1), this sum is equal to 22*4 = 88. However, this counts all x_i, but counts each corner square twice. Thus,

So the sum of the four corner entries is 10.
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