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:
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: