# WORHP Kata of July 2023: Queens puzzle ⌚ 2023-07-01

A kata (in the context of programming) is a small training unit to practise coding. In this series of**WORHP Katas**we present standard problems of optimization which you can use to get familiar with optimization (and our optimization software WORHP).

**Kata:**The queens puzzle is the problem of placing queens on an chessboard.

As an NLP, this could be formulated as follows:

- The optimization variables are the entries of a matrix
, where for
- means, there is a queen on position on the checkboard, and
- means, there is no queen on that position.

- The first set of constraints has to make sure, that in each column and in each row
- the sum of the entries is 1,
- (at least) one of the entries is 1.

- The second set of constraints has to make sure, that in each diagonal and subdiagonal
- the sum of the entries is not larger than 1.

*A solution will be provided with the next WORHP Kata.*

**Solution of last WORHP Kata:**The common approximations of the partial derivatives simplify on the given grid with spacing 1: