topic Re: Mathcad Community Challenge January 2026: The Art Gallery Problem in Mathcad

Mathcad Community Challenge January 2026: The Art Gallery Problem

DaveMartin — Thu, 01 Jan 2026 13:41:36 GMT

Happy New Year!

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

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.

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.

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?

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!

Re: Mathcad Community Challenge January 2026: The Art Gallery Problem

Werner_E — Thu, 01 Jan 2026 15:39:54 GMT

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:

Re: Mathcad Community Challenge January 2026: The Art Gallery Problem

AlanStevens — Mon, 05 Jan 2026 15:05:31 GMT

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

Alan

Re: Mathcad Community Challenge January 2026: The Art Gallery Problem

AlanStevens — Fri, 09 Jan 2026 10:26:00 GMT

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

Re: Mathcad Community Challenge January 2026: The Art Gallery Problem

DJNewman — Fri, 23 Jan 2026 17:04:10 GMT

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).

Re: Mathcad Community Challenge January 2026: The Art Gallery Problem

ttokoro — Sat, 24 Jan 2026 09:39:46 GMT

Using AlanStevens method, I make 5 guard positions answer.

The total area is 176400.

Change some positions and remove guard G_26,the uncovered area is 3.06%_.

But when remove guard G_27,the uncovered area is only 0.45% by 4 guards.

Removinf G₂, the blind area is 3.55% for 5 guards.

Re: Mathcad Community Challenge January 2026: The Art Gallery Problem

ttokoro — Fri, 30 Jan 2026 08:57:58 GMT

Just how to paint the answers.

Re: Mathcad Community Challenge January 2026: The Art Gallery Problem

ttokoro — Sat, 31 Jan 2026 11:07:17 GMT

Paint all.

Re: Mathcad Community Challenge January 2026: The Art Gallery Problem

ttokoro — Sun, 01 Feb 2026 00:00:32 GMT

Just few changes.

Re: Mathcad Community Challenge January 2026: The Art Gallery Problem

DJNewman — Mon, 02 Mar 2026 17:35:08 GMT

https://www.ptc.com/en/blogs/cad/mathcad/community-challenge-art-gallery-problem

Thanks for your participation in the January challenge!

Check out the March challenge now. 🙂