Tip of the hat to Tanya Khovanova for sharing this problem:
Is it possible to place seven points on a plane so that among any three of them, two will be at distance 1 from each other?
This comes from the 1978 Kyiv Olympiad for 7th graders! Yes, you heard me right: 7th graders. They have some exceptional kids there in Ukraine.
And adults, as we have been learning.