(quoted from post at 02:43:11 11/24/14) As others have mentioned, the correct answer is the cannon that fired straight up. People think that because the cannon ball lands 1 yard away from the cannon, it measured as a 1 yard shot. They totally forget about the 10,000 feet it went straight up and the 10,000 feet back to earth for a total of tiny smidge over 20,000 feet. The other shots make it farther away from the cannon but the total distance traveled by the cannon ball is less and that is the trick of the question.
I have had this conversation with a very socially awkward genius one time, he was drafted in the very early 1970s and being very smart realized that if he did well in artillery schooling, he could pick his placment. He was top of his class and picked the most dangerous assignment he could find... in California. Thats important because it ensured he could live to tell the tail of how smart he is, which he tried to not let too many days go by without doing....
Anyway, one time myself and another were talking ballistics for hunting/target rifles and Mr. Peabody gets drawn in just to tell us how to figure it out on paper using a slide rule. Cool but other than the challenge of figuring it out, he really didnt care (anti-gun pacifist). Eventually, the other guy I was talking to brought the question around to the very one being talked about, which of the 3 shots will travel the farthest. Well low and behold, Peabody not only knew the answer and how to figure it out but he had seen that group of questions at an interview as well as the other guy and started telling us all about it. Well Peabody was the type to tell you how to build a watch rather than tell you what time it is, even if I was just trying to be sociable when I engaged him, long story short, 4 beer later I had to get out of there and let him jabber away with the other guy.
To the point, the cannon fired straight up has the projectile that travels the farthest, even if it lands inches away from where it started. It also should be noted that the questions at the interview used to be quite common during the interview process although they seem to be a lot less popular now. Now, it think a persons personality at the interview is the most important thing. Go figure.
Just think, for 20 years I have been wishing I could have that hour and a half of my life back, only to find out it does have a small bit of relivance to real life... but to be fair, I did learn a little about .308 and steel silhouette shooting that day too so ya know, I got that going for me...