Deadlock

The enumeration walks every way the first five grabs can be interleaved — 3,125 of them — and then lets the system run freely to a fixed point. That is not the same as every possible schedule of the whole meal, which is unbounded. What it does establish is exactly what the page claims: of those openings, 278 reach a state from which nothing can proceed, and none do once the forks are numbered.

Taking the lower-numbered fork first works because it makes a cycle impossible: in any set of philosophers each holding one fork, one of them holds the highest-numbered fork in the set and is therefore waiting for nothing in it. Timeouts, backoff and retrying are not this. They make deadlock rarer and leave it possible, and this page does not model them.

Five philosophers is a loop over five entries in an array, and the interleaving is a list this page walks. There is no thread, no lock and no scheduler, so the page cannot show you a race — only why the counting rule is the right counting rule. A real system adds the part where you cannot see the state at all, which is most of what makes this hard.

This page cited EWD123, Cooperating Sequential Processes, as where the dining philosophers first appear. They do not appear in it: the archived copy in this repository is 109,280 bytes and contains the words philosopher, dining, quintuple and fork exactly nought times. What it does contain is the semaphore and the deadly embrace, which is why it is still cited. Dijkstra gives the history himself in EWD1000: EWD123 “was written in 1965 and served as lecture notes for my course in the fall semester of that year. (The problem of The Dining Quintuple —later dubbed ‘The Dining Philosophers’ by Tony Hoare— was the examination problem at the end of that semester.)” So the year is right, the document was not, and the familiar name is Hoare's rather than Dijkstra's. EWD198 works the problem under Dijkstra's name for it. An outside reader caught this on the live page on 2026-08-22. No gate here could have: every one of them checks that a cited document was fetched, not that it says what the page says it says.

A total order on the resource guarantees the group as a whole keeps moving. It guarantees nothing to any particular philosopher: with the right repeated schedule one of them can wait while the others eat, forever, and every check on this page stays green throughout because nothing is deadlocked. The two problems get confused constantly and they have different fixes — starvation wants fairness, a queue or a ticket, which this model does not have. Dijkstra's own solution used a semaphore per philosopher for exactly that reason.