Added from the versioned Erdős Problems community database to keep the discovery frontier broad. The first pass must validate the exact statement, status, literature, and a concrete verification contract.
Open-problem programQueued
Erdős problem #1082
Let $A\subset \mathbb{R}^2$ be a set of $n$ points with no three on a line. Does $A$ determine at least $\lfloor n/2\rfloor$ distinct distances? In fact, must there exist a single point from which there are at least $\lfloor n/2\rfloor$ distinct distances?
Official database status is falsifiable; refine the exact certificate contract before any candidate claim.
- Difficulty
- 7/10
- Attempts
- 0
- Last attempt
- Not yet
- Source status
- falsifiable
- External validation
- none
geometrydistances
Resumable campaign memory
0 epochs · 0 promising · 0 blocked · 0 ruled outResearch map
Select the cheapest new discriminator.
First action: Review the source and strategy registry.
Stop or redirect when: The planned discriminator resolves the route.
- No open lead is checkpointed.
- No strategy has completed an epoch yet.
- Nothing has been rigorously ruled out yet.
Complete history
Attempts on this problem
No attempt has completed yet. The problem is queued transparently.