Countdown Numbers Game Solver

I’ve been playing Summle for quite some time. It’s one of those daily puzzles where you share your results with your friends, and it takes the form of the numbers game from Countdown (or Letters and Numbers, if you prefer). For the unfamiliar, you’re given a three-digit target number and six smaller numbers from which to make it using only positive integer arithmetic.

A friend and I came up with our own version of “Hard Mode,” whereby we try to solve the daily puzzle as neatly as possible, with the subtotal from each step forming the left-hand side of the next step. This means that our Signal chat is littered with messages like this…

Me:

#Summle #1297: 4/4
⚪ 🔹 ⚪ = 🟡
🟡 🔹 ⚪ = 🟡
⚪ 🔹 ⚪ = 🟡
🟡 🔹 🟡 = 🟢

Apologies.

Them:

#Summle #1297: 4/4
⚪ 🔹 ⚪ = 🟡
🟡 🔹 ⚪ = 🟡
🟡 🔹 ⚪ = 🟡
🟡 🔹 ⚪ = 🟢
https://summle.net/

Yours is a bit messy

Me:

Oh, you swine!

There then follows a period of what I have recently learned is called incubation before the clean solution becomes apparent. This often involves going for a walk, run, bike ride, or cooking a meal.

#Summle #1297: 4/4
⚪ 🔹 ⚪ = 🟡
🟡 🔹 ⚪ = 🟡
🟡 🔹 ⚪ = 🟡
🟡 🔹 ⚪ = 🟢

Sometimes it’s the other way around and I find the clean solution.

Sometimes neither of us finds a clean way, and I cannot be sure whether no such way exists or whether it’s eluding us.

Until now.

Yesterday, I had a shower thought: what if I could determine whether there was a neat solution or “golden path,” programmatically, without revealing it? Revealing it would really spoil the fun.

And so my new Countdown Numbers Game Solver was born, and it’s now online for others to play with.

The ⭐ star icon in the solutions box indicates a “golden path” solution exists where each result flows into the next step. Today, this indicated I had some more work to do to avoid a gentle teasing.