When a group of colleagues discussed where their annual retreat should take place, they found that of all the colleagues: 12 would not go to a park, 10 would not go to a beach, 12 would not go to a cottage, 8 would go to neither a park nor a beach, 9 would go to neither a beach nor a cottage, 5 would go to neither a park nor a cottage, 4 would not go to a park or a beach or a cottage, and 5 were willing to go to all three places. what is the total number of colleagues in the group?

Given that 4 people would not go to a park or a beach or a cottage.

Number of people that will go to neither a park nor a cottage but will go to a beach = 5 - 4 = 1.

Number of people that will go to neither a beach nor a cottage but will go to a park = 9 - 4 = 5

Number of people that will go to neither a park nor a beach but will go to a cottage = 8 - 4 = 4


Number of people that will not go to a cottage but will go to a beach or a park = 12 - 5 - 1 = 6

Number of people that will not go to a beach but will go to a cottage or a park = 10 - 5 - 4 = 1

Number of people that will not go to a park but will go to a beach or a cottage = 12 - 4 - 1 = 7

Number of people willing to go to all three places = 5

Therefore, total number of colleagues = 4 + 1 + 5 + 4 + 6 + 1 + 7 + 5 = 33

Yes i could be the length of the triangle