Statement

In the recent festivities, Luca observed some kids playing in a gym. They seemed to enjoy very much moving around with all these colorful blocks, but sometimes they were unable to climb on them as they were too high when stacked! Consider this simplified representation of a typical situation: each block is a cube with all sides of one meter. Some cubes can optionally be stacked to form a heap and the heaps are aligned one next to each other, as in picture \reffigexample. When two heaps have the same number of cubes stacked, a kid can just walk to proceed to the next one. Similarly, in case of a descent when the next heap has fewer cubes than the current one, the kid exploits the gravity and falls gently on the soft cube. As gravity does not work in the reverse direction, kids cannot climb to higher heaps without the help of a ladder...