Equal Sums 3
Hints:
-
The total of the numbers in each circle is the same. Try adding all four circles together.
-
When you sum all four circles, you get the total of all the numbers (36) plus the four overlap regions (since each shared number is counted more than once).
-
Therefore, each individual circle adds up to:
Total of all numbers (36)+Sum of overlaps÷4\text{Total of all numbers (36)} + \text{Sum of overlaps} \div 4
That is: 9 + (Overlap Sum ÷ 4) -
The smallest possible overlap sum is: 1 + 2 + 3 + 4 = 10
The largest is: 5 + 6 + 7 + 8 = 26
But it must be divisible by 4. So the valid overlap sums are:
12, 16, 20, or 24 -
That means each circle’s total could be:
9 + 3 = 12,
9 + 4 = 13,
9 + 5 = 14, or
9 + 6 = 15 -
This narrows down the possibilities and gives you a solid place to start!

