Using your Head is Permitted

December 2016 riddle

The following riddle comes from Dominic van der Zypen. (Thanks, Dominic!)

The parliament of Prepostria has n>2 members. For its various tasks, the parliament uses multiple committees, each composed of a subset of the parliament members. Due to recently passed bills, the committees have to abide by the following rules:

  1. Every committee must consist of at least two members of parliament.
  2. Any two distinct committees must have exactly one common member. (This is to minimise overlaps while facilitating inter-committee communication.)
  3. Every member of parliament must be in at least two committees. (They cannot be too lazy.)

As a function of n, what is the maximum possible number of Prepostria's parliamentary committees?

As usual, all answers must be accompanied by proofs.

List of solvers:

Hanlin Ren (1 December 19:46)
Kuan Yang (2 December 03:36)
Lin Jin (2 December 17:29)
Tianyi Zhang (3 December 00:31)
JJ Rabeyrin (3 December 09:01)
Radu-Alexandru Todor (6 December 08:19)
Teng Li (22 December 07:30)
Oscar Volpatti (31 December 00:31)

Elegant and original solutions can be submitted to the puzzlemaster at Names of solvers will be posted on this page. Notify if you don't want your name to be mentioned.

The solution will be published at the end of the month.


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