Question

In the following figure, four overlapping shapes (rectangle, triangle, circle, and hexagon) are given. The sum of the numbers which belong to only two overlapping shapes is ________.

 

Hint:

Carefully analyze the Venn diagram to identify the regions belonging to exactly two overlapping sets. Ensure all numbers within those regions are included in the sum. Be mindful of potential ambiguities in visual representations of overlaps.

Answer 1

We analyze each number based on how many shapes it overlaps with:

1: Belongs to {circle, rectangle, hexagon} → 3 shapes (Not counted)
2: Belongs to {circle, rectangle} → 2 shapes (Counted)
3: Belongs to {circle, rectangle, triangle} → 3 shapes (Not counted)
4: Belongs to {rectangle, hexagon} → 2 shapes (Counted)
5: Belongs to {circle, triangle} → 2 shapes (Counted)
6: Belongs to {circle, triangle, hexagon} → 3 shapes (Not counted)
7: Belongs to {circle, triangle} → 2 shapes (Counted)
8: Belongs to {circle, triangle, hexagon} → 3 shapes (Not counted)
9: Belongs to {circle, triangle, hexagon} → 3 shapes (Not counted)

So, the numbers that belong to only two shapes are: $2, 4, 5, 7$

\[ \text{Required sum} = 2 + 4 + 5 + 7 = \boxed{18} \]