Sunken Treasure: Visualizing the Knapsack Problem with Geometric Selection

This example uses the “sunken treasure” metaphor to demonstrate the knapsack problem: selecting an optimal subset of items when a capacity (constraint) limits what you can carry. It highlights the core ideas of combinatorial optimization, constrained selection, and reasoning about achievable best outcomes. In the construction, GeoGebra’s Flatten and Polygon commands are used to restructure and render the graphic elements—flattening nested/grouped objects into a usable set and drawing polygonal outlines for clear item/option visualization. The model includes multiple item objects (e.g., watch, teapot, statue, ring, perfume, mirror, key, harp, cutlery, compass, coins, bell, candlestick, necklace, glasses) together with box/container variants (boxes and box*) and interactive selection states (select*), emphasizing which items become candidates under different choices. Suitable for middle/high school learning, introductory optimization units, and teaching where visual intuition helps explain knapsack-style decision making.