The aim of the study text is to motivate current and future teachers to develop combinatorial thinking in (not only) primary school pupils. In particular, the material presented contains various themes and tasks that can be used - often in the form of a game - as a tool to promote combinatorial reasoning. Solving combinatorial problems promotes the development of systematic thinking and generally leads to thinking things through. Combinatorial skills allow solving problems in various fields of human activity such as chemistry, physics, history, biology or sociology. Specifically, the ability to solve combinatorial problems enables one to succeed as a programmer. We will divide the ways of developing combinatorial thinking into three main parts (using word problems, using graphical problems and using games). Special attention will be paid to mathematical chess problems. The author has collected in the study support problems which, in his opinion, are nice and could help pupils to develop their combinatorial skills in a fun way.