Mai's friends and lovers were all invited for the *Valentine's Day* party. After enjoying the wonderful love music and meal, she believed that it's the great idea to play the heart-counting game. The dialogue started:

**Mai**: The shape is counted as one *heart* if:

- Two adjacent sectors in a heart are either tangential or intersecting.
- The projected lines are tangent to the sectors.

**Yugi**: That seems quite interesting.

**Tea**: I am not even good in discrete mathematics, so I am SO bad in counting. Since I believe you are so good in mathematics, you should figure out the best method to answer Mai's problem! There isn't any reason why I would find another man to love! :)

**Mai**: The couple who arrives with the correct answer first wins the game and earns a grand prize! The time starts now!

*[Mai revealed the image as shown above. After few seconds..]*

**Yugi**: I have the answer, and I am very sure it's correct! *[Answer hidden]*

**Mai**: We have a winner!

**Tea**: Wow! What a versed skill you have here! You are the true Valentine mathematician!

How many hearts in all did he find?

**Note:** Assume that the common circular sectors have same area, and that the 14-sided polygon is regular.

*This is the fifth chapter of the story. Check the following chapter directory if you are interested:*

×

Problem Loading...

Note Loading...

Set Loading...