Here we go..! Better late than never.
TOOLS USED: Unity, Inkscape, GIMP, Audacity.

Play the game here: https://ldjam.com/events/ludum-dare/42/prime-planets
THEME ANNOUNCEMENT:
I liked the new 11am (BST) start time since I could (in theory) come up with some amazing idea and sleep on it. Alternatively, it could make my brain not sleep. It did that.
I expected 'Fragile', 'Decay' or 'One minute' to win, and had some ideas for those, which were of course now useless. My initial thought was (as usual...) to imagine some 3d physics craziness in Unity, maybe using a swarm of nav agents chasing / being chased.
I vowed this time to not enter Ludum Dare unless its a game idea I really really want to make. Either the mechanics or use of theme had to really grab me.
SATURDAY
Prototyped the physics/nav agent thing. I thought the swarm of nav agent blobs could later be cats. I was going out all afternoon, but anyway, I had some blobs navigating a super-simple maze, with walls to block them. I added some jump code to see if they'd pile on top of eachother and get over the walls, but I soon discover that mixing nav agents and physics is pretty awkward. I later added some boxes, thinking the player could move these into place, as the room shrunk perhaps. Kinda worked, but very glitchy. Moveover, wouldn't every level be the same? ie move boxes into place, wait for cat glitching to occur.
As mentioned above, this didn't seem to be a game I really wanted to make, or one that would even be playable. Went out on my trip, kinda giving up on the original idea and jam altogether. In the evening I browsed the site, seeing many fantastic games well underway.
SUNDAY
A thought occured to me: I could make a maths game (note - I'm a maths & computing teacher). I get to see various maths resources over the years. Dice/number games are some of the most common, so I don't claim a lot of originality, but I did my best to add my spin on everything. A space theme would work really well, and you 'run out of space' in many board/puzzle games as the board fills up.
From this point, I was really productive. The requirements of the game code are very clear, and theres no major stumbling blocks to making a 2d puzzle game like this.
-- Early progress getting the board set up.
The hardest bit was the computer AI, which in the end is a brute-force checking of all combinations of numbers and operations.
It wasnt realistic to hit the Compo deadline, so for the first time I entered the Jam. It did have the advantage of allowing me to grab some graphics and audio from elsewhere.
WHAT WENT WELL
Completed the game fully, nothing major got cut though proper help/menus would've been nice. I could also add a 'hint' option, that would be cool. As would difficulty levels. But overall, scope was just about perfect for 2 days.
By entering the Jam I could spend most of my time on coding. Creating audio is never my strong point, but I think the sounds combine quite well.
The AI took ~50% of the time to code, and many bugs were squashed. It was challenging but never frustrating to code.
WHAT DIDN'T GO SO WELL
Struggling on Fri/Sat, brainstorming ideas. Not just re-treading my usual go-to ideas. Need to be better at 'thinking outside of the box'. Hence, started too late for the Compo.
Very little time for testing, resulted in a bunch of bugs, which early testers spotted. One major bug let the AI cheat, so I did patch that one asap.
-- One of many bugs, now fixed...
Technically, JS/HTML5 would've been fine for this game (and its output usually plays well on iPad), but I'm very rusty with that tech (e.g. Phaser), so went with Unity.
Overall, I enjoyed being so productive and making a game that turned out well (imo), and I find fun to play myself.