  In this paper, we relate Viterbo's conjecture from symplectic geometry to
Minkowski versions of worm problems which are inspired by the well-known Moser
worm problem from geometry. For the special case of Lagrangian products this
relation provides a connection to systolic Minkowski billiard inequalities and
Mahler's conjecture from convex geometry. Moreover, we use the above relation
in order to transfer Viterbo's conjecture to a conjecture for the longstanding
open Wetzel problem which also can be expressed as a systolic Euclidean
billiard inequality and for which we discuss an algorithmic approach in order
to find a new lower bound. Finally, we point out that the above mentioned
relation between Viterbo's conjecture and Minkowski worm problems has a
structural similarity to the known relationship between Bellmann's
lost-in-a-forest problem and the original Moser worm problem.
