16-Pearl

Question

Mathcad Community Challenge January 2026: The Art Gallery Problem

Forum|Forum|3 months ago
January 1, 2026
5 replies
495 views

Happy New Year!

This month’s challenge is inspired by recent events: the October 2025 Louvre heist in Paris France.

Cour_Marly,_Musée_du_Louvre_from_Paris.jpg

Using Mathcad Prime, solve any or all of the following challenges:

Challenge 1 (Polygonal): find the minimum number of guards necessary to cover 100% of the following polygonal space.

To be unobtrusive, the guards must be placed at vertices. The guards are inside the museum. Assume that the guards can turn their necks and bodies to see everywhere around that point that is not blocked by a wall. The guards have excellent vision and can see everything clearly between them and a wall.

Art Gallery Polygon v2.png

Challenge 2 (Graphing): using the plotting and charting capabilities of Mathcad, depict the placement of the guards and their zones of coverage.

Challenge 3 (Orthogonal Variant): find the minimum number of guards for the following art gallery.

Art Gallery Orthogonal v2.png

Challenge 4 (Graphing): Depict the placement of the guards and their zones of coverage for the orthogonal variant.

Challenge 5 (Basher Tarr variant): You are the tech expert for the Ocean’s 11 crew. Your job is to remove one guard to leave the maximum amount of exposed area. Which guard do you remove in either of the scenarios?

Oceans 11.jpg

Note: Creo Parametric 7.0 CAD part models and a Mathcad Prime 10 worksheet have been attached. If people want to incorporate Creo into their solution, feel free. The Mathcad worksheet contains matrices of the vertices.

Find the Mathcad Community Challenge Guidelines here!

1_Art-Gallery-Problem---Vertices.zip

2_Creo-7-Part-Models.zip

W

Werner_E

25-Diamond I

There seems to be an error in the vertices table. Although a number of dimensions are missing in the Creo screenshot, fortunately the relevant one is specified:

A

AlanStevens

19-Tanzanite

Here's my simple starter for the polygonal version only.

Alan

1_January2026Challenge_AS_1.zip

A

AlanStevens

19-Tanzanite

Here's a similar approach to the Orthogonal case:

As before, the positions of the guards is not unique, and I haven't indicated overlapping fields of vision.

In both cases I just used a visual approach, as I haven't figured out an algorithmic one. I'd be interested to see if there is one.

It's not clear to me if the question is looking for a positioning with minimal overlapping fields of vision - if so, I haven't tried to find that!

I guess the last part (Challenge 5) will require the actual calculation of areas - something I've tried to avoid so far!

Alan

D

DJNewman

18-Opal

While it may be good for the museum for no one to try Challenge 5, it's way more fun if someone does try it! (And good as a mental exercise.)

Anyway, January surprisingly ends in a week. Maybe for those snowed in the United States this weekend and looking for a wholesome activity to do, the challenge would be fun to try solving (if you have power).