Time allotment - time management
15 minutes in one class, more if you permit discussion to wander or if you introduce physical objects and permit a great deal of conjecturing.
Students will debate the reasonableness of Alice's conjecture and be pressed to conjecture another approach, e.g., cutting wider sections at end or in the middle.
Even more time can be used if you pose the problem as open ended without positing the cutting scheme offered above.