Problem 3 · Count shared endpoints and gaps · 3 points
Made by AI and not reviewed by a real person.
A rectangular garden has posts 2 m apart around its edge and along a fence joining the midpoints of its long sides, with posts at every corner and at both ends of the middle fence. There are 47 different posts in all, and each long side has 13 posts; how long is a short side?
- 12 m
- 20 m
- 18 m
- 14 m
- 16 m
Show a hint
- Think about which posts would be counted twice if you counted each stretch of fence separately.
- Count the posts on both long sides first. Where must the remaining posts be?
Show the answer and solution
Answer: E — 16 m
The two long sides have 26 different posts, leaving 21 posts between them. These lie along three equally long stretches: the two short sides and the middle fence. Each stretch has 7 posts between its endpoints, making 8 gaps of 2 m, so a short side is 16 m. The tempting 14 m counts the 7 posts between the endpoints as 7 gaps instead of 8.