Taking a cue from two recent articles of S. Innamorati et al., [9] and [10], as part of promoting and improving pattern discovery skills among students, the construction of the (11, 3)−arc configurations of the projective plane of order five can be used as example of a problem solving task. We show that answering to the question of how to construct the maximum (k, 3)−arcs in PG(2, 5) opens the door to a wealth of interesting mathematics.