The Chasam Sofer's Reason For The Yom Tov Of Tu B'Av
כתיבה וחתימה טובה
The Gemara's Explanation
The Gemoro (Moed Katan 9a) says on the Pasuk (Melochim 1:8:64):
וילכו לאהליהם שמחים וטובי לב
לאהליהם
They came home and their wives were Tehoros.
וטובי לב
They all became pregnant with a Ben Zochor.
על כל הטובה
They were forgiven for eating on Yom Kippur.
The Timing Of Tu B'Av
The last person to reach his home in Nehar Peros was on the 7th of Cheshvan (Ta’anis 10a).
If you count from the 7th of Cheshvan, 271 days of pregnancy (Nidah 38a), they will have given birth on the
15th of Av
which was their sign of Kaparah.
The Chasam Sofer's Additional Reason For The Simcha
According to the Chasam Sofer, perhaps we can add an additional Simcha on Tu B'av.
They all had boys
and realized that in a few years from then there won't be any more a Shidduch crisis.
* גימטריה חמשה עשר באב
** (Drashos 1:P43)