Four measurements form the chain M > N ≥ O = P. What is the strongest conclusion that can be drawn about M and P?

Compose the chain: M > N, N ≥ O, O = P. The equality carries O's relation over to P, so the chain reduces to M > N ≥ P. A strict link followed by a non-strict one composes to strict, so M > P. That is the strongest of the four because 'M ≥ P' and 'M ≠ P' are both true but each says less than M > P — they are the traps for a solver who lets the non-strict link N ≥ O dilute the strict opening link, and for one who spots only that the two cannot be equal. 'Cannot be determined' is what a solver concludes who treats the equality O = P as breaking the chain rather than passing it through.