When a group of colleagues discussed where their annual retreat should take place, they found that of all the colleagues: 17 would not go to a park, 24 would not go to a beach, 13 would not go to a cottage, 8 would go to neither a park nor a beach, 3 would go to neither a beach nor a cottage, 2 would go to neither a park nor a cottage, 1 would not go to a park or a beach or a cottage, and 8 were willing to go to all three places. what is the total number of colleagues in the group?

We're assuming e.g. the two that won't go to P (park) or C (cottage) includes the one that won't go anywhere.

Let's call the three rings of the Venn diagram
 
We'll label the eight regions like , here meaning in P, in B, not in C.

1 would not go to a park or a beach or a cottage



8 would go to neither a park nor a beach.  We have to take away the one guy who won't go anywhere to find out how many go just to college.

 

 

3 would go to neither a beach nor a cottage,

 

2 would go to neither a park nor a cottage, 

 

17 would not go to a park





24 would not go to a beach



13 would not go to a cottage
 


8 were willing to go all three places.



Adding them all up,