Here's a "cute" little problem involving weighing "circles, squares and stars." Enjoy!

Scroll down for solution after you've worked on it.

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The following approach will make sense only if you know what a "matrix" is and what the determinant of a matrix is. Click the link below to see a video on computing the determinant of a 3x3 matrix. Scroll past this to see an alternate method which does not use matrices.

http://www.youtube.com/watch?v=21LWuY8i6Hw

Alternate solution:

a = circle  b = square  c = star

equation #1     a + 3b = 2c
equation #2    3c + 3b = 6a

dividing #2 by 3 we get

                c + b = 2a

equation #1 moved around becomes

                a - 2c = -3b

equation #2 moved around becomes

              -2a + c = -b

so we now have

                a - 2c = -3b
              -2a + c = -b

adding these 2 equations together

               -a - c = -4b

dividing by -1 we get

                a + c = 4b

circle + star = 4 squares