Abstract
The paper introduces several tasks from a currently developed teaching resource focused on high-school combinatorics. The prepared material uses tasks to build up combinatorics.
Such challenges come before theory is explained and phenomena are given their names. In this paper we present tasks that revolve around counting paths in between cities.
We use these tasks to demonstrate both basic combinatorial principles (rule of sum, rule of product) and the more advanced ones (e.g. relations in the Pascal triangle). The paper shows the variety this path "environment" offers and presents different strategies for solving such problems.
These can be used in class both at secondary and elementary level of education.