Why your first solution is never the best one
Solving is the easy half. The interesting half is everything you do to the solution afterward.
by Laurens Dauchy, Builder of 5q0Your first working solution is a draft: it proves the problem can be solved, and almost nothing more. The real game in an optimisation puzzle is the compression pass, going back to make that draft cheaper, faster or smaller. 5q0 is built around this, scoring every solution so you can see how far your first answer is from a good one. Learning to solve first and optimise second, in that order, is the core skill, and rushing to optimise before you have solved is the common mistake.
In an ordinary puzzle, the first solution is the last one, because reaching the answer ends the game. In an optimisation puzzle it is the opposite: your first working solution is where the real game begins, and it is almost never any good, on purpose. It proves the problem can be solved and little else, because you built it to run, not to run well. The place this is clearest is 5q0, which scores every solution the moment it works and quietly shows you how far your first attempt sits from a good one. This article is about why the first answer is only a draft, what the second pass actually involves, and why doing them in the right order is the whole skill.
The two different jobs
Solving and optimising are separate jobs that happen to use the same board. Solving answers a yes-or-no question: can this be done at all? Optimising answers a how-much question: how cheaply, how quickly, how compactly? These are not the same skill, and trying to do both at once is why so many attempts stall. When you are still figuring out whether a machine can work, every part is provisional, and polishing a provisional part is wasted effort because it may not survive.
This maps onto how problem solving works generally: you first find a path to the goal, then refine it. The first path is rarely efficient, because finding any path at all takes all your attention, and efficiency is a luxury you can only afford once the path exists. A first solution that looks clumsy is not a failure, it is a first solution doing its actual job, which is to prove the thing is possible.
What the first solution really is
It helps to be precise about what you have when a machine first runs. You have an existence proof. You have learned that the puzzle is solvable, you have learned roughly what shape a solution takes, and you have learned where the hard parts are. Those are valuable, and they are all you have; the specific machine in front of you is usually oversized, slow, or wasteful, because none of those things mattered while you were making it work. The table lays out the gap honestly.
| Property | Your first solution | A good solution | The gap |
|---|---|---|---|
| Works | Yes | Yes | None; both run |
| Cost | Whatever it took | Deliberately minimised | Often large |
| Cycles | Usually slow | Tuned | Often large |
| Footprint | Sprawling | Tight | Often large |
| What it taught you | The puzzle is solvable | How to solve it well | The whole game |
The last row is the important one. The first solution’s real output is not the machine, it is the understanding, and that understanding is what you spend on the second pass.
The compression pass
The second phase has a name worth adopting: compression. You take the working solution and squeeze it, making it smaller, cheaper or faster while keeping it working. This is where the craft lives, and where experienced players spend most of their time, because it is genuinely more interesting than the first solve. The reason it is interesting is that every squeeze is a decision: you are moving along the Pareto front, trading one score for another, and choosing which trade is worth it.
The practical method is to chase the free wins first. Some improvements cost nothing, a redundant part removed, a wasted step cut, and those are pure gains you should take before anything else. Once the free wins are gone, every further improvement is a genuine trade, part of the multi-objective optimisation that the three-way tradeoff covers in full, where cost, cycles and footprint fight each other. That is when compression becomes a real puzzle of its own, often harder and more rewarding than the solve that preceded it.
The order matters more than anything
Here is the single most useful habit: solve first, optimise second, and do not blur them. The most common mistake in an optimisation puzzle is trying to optimise before there is anything to optimise, polishing individual parts of a machine that does not yet run. It feels productive and it is not, because you are refining pieces that may not survive the design. Get something working first, however ugly, then optimise the whole thing once it exists.
This is easier said than done, because the instinct to make each piece neat as you place it is strong. Resisting it is a skill in itself. In 5q0 the discipline is helped by the fact that you can always keep a working version and experiment freely from there, so there is no risk in tearing a solved machine apart to rebuild it better. Solve, save the fact that it works, then compress without fear.
When the first solution is good enough
None of this makes optimising mandatory, and it is worth saying so. If you only wanted the puzzle solved, the first working solution is good enough, full stop, and stopping there is a legitimate way to play. The compression pass is for when a level has caught your interest and you want more from it, not a tax you must pay to move on. In 5q0 every level can be finished on first solutions alone, and the scores are an invitation rather than a requirement. Good enough is a real answer, and knowing when to accept it is its own kind of wisdom.
Key takeaways: the first solution is a draft
Your first working solution proves the problem is solvable and almost nothing more; it is a draft, built to run rather than to run well. The real game is the compression pass, taking that draft and trading cost, cycles and footprint against each other to make it good. The order is the skill: solve first, optimise second, chase the free wins, then make deliberate trades. 5q0 is built around exactly this, scoring every solution so the gap between your first answer and a good one is visible and inviting. And when good enough is all you wanted, good enough is where you are allowed to stop.
Quick answers
Why is your first solution never the best one?
Because a first solution is built to work, not to be efficient, and those are different goals. Your first machine in 5q0 proves the puzzle is solvable and usually little else: it is oversized, slow or wasteful because you were focused on making it run at all. The best solutions come from a second pass that trades cost, cycles and footprint against each other on purpose, which you can only do once something works.
What is the compression pass in a puzzle game?
The compression pass is the second phase of solving, where you take a working solution and make it smaller, cheaper or faster without breaking it. In 5q0 this is where most of the game lives: you have a machine that runs, and now you rebuild parts of it to spend fewer resources. Solving proves it is possible; compression is the craft of doing it well, and it is the part experienced players enjoy most.
Should I optimise my solution as I build it?
Usually no. Trying to optimise before you have anything working is the most common mistake, because you are polishing pieces that may not survive the final design. In 5q0 the reliable order is to get any machine running first, however ugly, then optimise the whole thing once it works. Solve first, compress second: optimising a solution that does not yet exist just slows down finding one that does.
How do I get better at optimising solutions?
Separate the two phases and give each its full attention. First solve without judging efficiency, then optimise without fear of breaking things, because you can always return to the working version. In 5q0, chase the free improvements first, the ones that cost nothing, then start making deliberate trades. The skill grows fastest when you stop trying to do both at once and treat compression as its own distinct, enjoyable pass.
When is the first solution good enough?
When you only need the puzzle solved and do not care about the score, the first working solution is entirely good enough, and there is no shame in stopping there. Optimisation is optional. In 5q0 you can finish every level on first solutions alone; the compression pass is for when you want more from a level, not a requirement to progress. Good enough is a legitimate place to stop.