Identical shapes have equal values
In Shape equation puzzles, each shape stands for a number. Every copy of that shape has the same value within a puzzle, and both sides of each equation are equal.
Two circles total 8. Because they have equal values, each circle is 4. The practice may write this as 2 times a circle rather than showing two separate circles.
Start with a balance that contains only one kind of shape. Divide the total equally between its copies.
Replace the known shape
The first balance gives a circle value of 4. Use that same value in the second balance: 4 plus the square equals 11.
Subtract 4 from both sides. The square must be 7. Check by putting the values back: 4 plus 4 is 8, and 4 plus 7 is 11.
Do not divide 11 equally here. Different shapes can have different values. Only identical shapes are guaranteed to match.
Find the value that fits both balances
This is a new puzzle, so the shapes may have new values. Two circles now total 6. One circle and one square total 11.
Work out the circle first. Substitute it into the second equation, then check that your square value keeps both balances equal.
Try it
What is the value of the square?
- 8
- 14
Show the answer
8
Each circle is 3 because two circles total 6. The square is 11 minus 3, which is 8. Substituting 3 and 8 makes both equations true.
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