Here is a curious grid! The sums of the shapes are shown at the end of each row, and at the bottom of each column.
What is the missing sum, and what is each shape worth?
Puzzle Copyright © Kevin Stone
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Hint
Look at the first and third columns first.
Answer
40.
Circle = 12
Star = 3
Square = 7
Triangle = 9
Reasoning
Looking at Column 1 and Column 3 we have:
[1] Square + Star + Circle + Square = 29
[2] Square + Square + Triangle + Star = 26
If we subtract [1] - [2] we get:
[3] Circle - Triangle = 3
And Row 3 is:
[4] Circle + Circle + Triangle + Circle = 45
If we add [3] + [4] we get:
Circle + Circle + Circle + Circle = 48
So Circle = 12.
Using [3] we find that Triangle = 9.
Using Column 2 we find that Star = 3.
Using Row 1 we find that Square = 7.
Double-Checking
The rows add to: 35 + 26 + 45 + 25 = 131.
The columns add to: 29 + 36 + 26 + 40 = 131.
The rows and columns must add to the same number, so this could have been used a shortcut to the missing sum.
In total, there are:
5 Squares = 5 x 7 = 35
5 Circles = 5 x 12 = 60
3 Stars = 3 x 3 = 9
3 Triangles = 3 x 9 = 27
Which is also a total of 131.
So all of the totals are the same, as expected.
