A Weekender number is, for any integers k ( > 1) and n ( > 0)
W = ( n / 2 ) ( ( ( k – 2 ) n ) + 4 – k ) where W is divisible by k
k is described as the order of the Weekender number. W/k is the count.
There is a trivial solution, W = k for any k, when n = 1.
Weekender numbers of count <= 8 are considered feasible.
The Weekender Theorem is that there are no non-trivial, feasible Weekender numbers of order > 8. I believe there is a proof of this, but it currently escapes my recollection.
Weekender numbers were first proposed by Patrick Heesom and Rupert Morrish ~1992 as an exercise in arranging beer bottles in k-gons where k drinkers are drinking equal numbers of beers.