Freiman Duel — Sumset Showdown

Red and Blue draft numbers. Smaller self-sum wins.

Turn: Red

Draft Pool (1–20)

How to Play

  • Red goes first. Players alternately pick distinct numbers from 1 to 20.
  • Each player selects exactly four numbers: Red builds A, Blue builds B.
  • After eight picks, the game compares A + A and B + B (all pairwise sums with repetition, duplicates removed).
  • The player with the smaller self-sumset size wins. If equal, it is a tie.

Freiman’s Theorem (informal)

In the integers, a finite set with a small sumset has strong internal structure: it is contained in a low‑rank generalized arithmetic progression of comparable size. In short: small self‑sum ⇒ structured set.