How to solve Sum Path puzzles

Cross the grid from corner to corner. The numbers you step on must add to the target exactly.

You move only right and down, from top-left to bottom-right, and the cells you land on must sum to the target.

Work from the target's distance to the floor

The most useful first step is to find the cheapest possible route — at each point, the smaller of the two onward options, roughly speaking. That gives you the minimum any route can achieve.

Now compare the target to that floor. If the target is only slightly above it, your route is nearly the cheapest one, and every expensive cell is effectively forbidden. That converts a search over many routes into a short list of small detours.

Prune with remaining sums

Partway along, subtract what you have collected from the target. What remains must be achievable from your current position — and it cannot be less than the cheapest onward route from here, nor more than the dearest. If your remaining budget falls outside that window, this path is dead and you should back up.

This is the difference between solving these puzzles and flailing at them.

Why routes are short

These puzzles are deliberately smaller than they could be, and the reason is worth stating. On a 6×6 grid a route crosses eighteen cells, and the number of distinct routes is large enough that thousands of them share the same total. A puzzle built that way looks fine and has many solutions — broken, but invisibly so.

Targets near the cheapest crossing are provably unique, and verifying that is fast. The consequence is shorter routes and smaller grids, which is a real cost, accepted deliberately rather than hidden.

Frequently asked questions

Can I move diagonally or upward?

No. Only right and down, which is what keeps the number of routes tractable and the puzzle verifiable.

Why are the grids small?

Because uniqueness is verified, and on larger grids the number of routes sharing a total grows quickly. A bigger grid would mean puzzles with several valid answers, which is worse than a smaller grid with one.

Is there always exactly one route?

Yes. Every puzzle is checked to have a single route hitting the target before it is offered.