Four chess pieces

The workings

Fun & games in the working is taking a short (and well-deserved?) Christmas break; we’ll be back in the new year. To spend the holidays we thought we would talk about chess. And speaking of chess in Seville, it is impossible not to remember the exciting 1987 World Chess Championship, held in the Lope de Vega theatre. It was the critical point in the rivalry between Anatoly Karpov and Garry Kasparov, which aroused enormous attention for chess in Spain (attention almost unknown until then, with a few honourable exceptions), and whose political nuances are also very interesting. In this divertimento, we will not ask to play at the level of the two ex-Soviet grandmasters, but we will certainly have to think with some pieces (how many remains to be seen) on the chessboard.

The fun

A chessboard has size \(n \times n\), with \(n >1\). What is the smallest number of pieces that must be placed on the board to ensure that four of them determine a parallelogram?

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Solution

We encourage the readers to try to solve the divertimento for themselves. Whether you succeed or not, you can always consult the solution in this link.