The anthology consists of three novellas. Invitation to Murder.
A man who is entirely dependent on his uncle to provide for his living (at least he is honest about it) was worried that one of the three young women working for his wealthy relative his matrimonial plans for the latter which would put his income source in great peril. He asked Nero Wolfe to find out which one of the three is the threat. The detective thinks Archie Goodwin is a great expect on women and Archie himself shares this delusion, so off he went to investigate.
Most of Wolfe's investigations are related to murders, and this time he was not disappointed as Archie soon stumbles upon one. In fact things became so intense Wolfe who practically never gets outside has to do it this time: the mystery was quite complicated and required his personal presence. The Zero Clue.
The plot strongly relates to that of Isaac Asimov's Foundation. Both of these were written at approximately the same time when the idea was popular. A college professor discovered a statistical formula which allowed him to calculate the probability of human behavior and make fairly accurate predictions of various events. He was so successful that he quit his job and began his scientific oracle work - so to speak - full time making big money.
One day his was found murdered, but not before he left a clue indicating Nero Wolfe might help with the identity of culprit and $500 dollars as a fee for detective's services. Wolfe thinks it should be easy money and decided to solve the mystery.
This novella contains an interesting bit on the history of mathematics related to one of the most important discovery - extensively used in modern life - in the field during the time when none of the modern nations existed. This Won't Kill You.
To make a long story short, Nero Wolfe broke his habit of never leaving his house and went to see a baseball game only to find out it was fixed in the blatantly obvious way and one of the most promising rookie players murdered. The team owner asked Wolfe to investigate the crime and Archie Goodwin whose favorite team just lost an important game due to a foul play is happy to help.
This is a unique story in sense that both Nero Wolfe and Archie Goodwin solved the mystery at the same time independently using different approaches. The former used his deductive skills and the latter legwork and nosiness which actually put his life in a real danger. By the way the mystery was very simple and obvious once Wolfe explained it, but there were enough red herrings to keep it hidden.
The final rating is my usual 4 stars for a book of the series.