Each of the four shapes represents a positive whole number. The sum of the shapes in each row and column is displayed at the end of each row and column. Using this information, determine the numerical value of each shape.

9514 1404 393

  A = pentagon = 6

  B = 5-pointed star = 8

  C = rectangle = 4

  D = spiral = 3

Step-by-step explanation:

Starting in the upper left corner, name the shapes A, B, C, D clockwise in the 2×2 square in that corner. Then we have ...

  A = pentagon

  B = 5-pointed star

  C = rectangle

  D = spiral

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It turns out to be convenient to look at rows and columns with two of each shape.

  Row 2: 2(C+D) = 14   ⇒   C+D = 7

We can use that in column 2 to find B:

  B +C +B +D = 23   ⇒   2B +(C+D) = 23   ⇒   2B = 16   ⇒   B = 8

This lets us find D:

  Row 4: 3D +B = 17   ⇒   3D +8 = 17   ⇒   3D = 9   ⇒   D = 3

So, C can now be found:

  C+D = 7   ⇒   C +3 = 7   ⇒   C = 4

Finally, we can find A:

  Row 1: A +2B +D = 25   ⇒   A +2(8) +3 = 25   ⇒   A = 6

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In summary, the numerical values are ...

  A = pentagon = 6

  B = 5-pointed star = 8

  C = rectangle = 4

  D = spiral = 3