SumSlide · strategies

Endpoints first.

The split points are determined by cumulative sums — a small running total instantly narrows where dividers can go.

Prefix sums

The first target tells you what the first segment sums to. Scan from the left: the moment the running total hits the target, that's the only valid split point for the first divider.

Strip 4,3,5,2,1,6 with first target 12. Scanning left, 4+3+5 = 12 — the divider drops right after the 5 (ringed).

Suffix sums

Same logic from the right: the last target constrains the last segment. Lock both ends and the middle has fewer options.

Same strip, last target 7. Scanning right, 1+6 = 7 — the final divider drops just before the 1 (ringed).

Process of elimination

With endpoints locked, the middle tiles are a smaller subproblem. Apply the same prefix/suffix trick recursively.

Both ends locked (12 | · | 7), the lone middle 2 is all that's left — the third group resolves itself.

Ambiguity check

If two prefix sums both hit a target (e.g. 3+6=9 and 3+6+0=9), the uniqueness guarantee means the OTHER constraints (column / later targets) will resolve it. Check both and discard the one that breaks a later target.

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