MATH STINGER #97
by Dr. Joel C. Fowler
Associate Professor of Mathematics
The puzzle for this issue relates to an old problem involving two crossed ladders of unequal length leaning against the vertical walls of an alley. Suppose that the base of each ladder is on the ground against opposite walls, with their tops against the other wall, some distance up. Thus the two ladders cross some distance above the ground to form a lopsided X. The classic puzzle is to find the width of the alley given the lengths of the ladders and height of the crossing point. Instead, the puzzle for this issue is to find the smallest set of integers for the ladder lengths and alley width that make all distances involved in the problem integers. That is, the ladder lengths, alley width, crossing point height, distance each ladder reaches up the walls, lengths along each ladder from each end to the crossing point, and horizontal distance along the ground from each wall to the point on the ground directly below the crossing point must all be integers. Note that the ladders must be of unequal length.