A New Development of the Classical Single Ladder Problem via Converting the Ladder to a Staircase

Our purpose is to shed some new light on problems arising from a study of the classical Single Ladder Problem (SLP). The basic idea convert SLP corresponding Staircase Problem. main result (Theorem 1) shows that this works fine and results can be obtained by just calculating rational solutions an algebraic equation. Some examples such concrete calculations are given also given. In particular, we derive number integer SLPs with congruent ladders, where set rectangular boxes sides constitutes staircase along common ladder. Finally, case regular ladder investigated illustrated examples.