Start at the target, not the start.

Invert the last edges: a final +7 into the target means the previous node held target − 7; a final ×2 means it held target ÷ 2 — and if the target is odd, that ×2 edge is impossible, cross it off without computing anything else. Walking two steps back usually leaves a single live entry point.

Before tracing paths, compare start and target. Only + and − in the maze? Then the target must be reachable by a plain sum of the edge operands — check parity: additions and subtractions of the operands fix whether the result can be odd or even. Target far bigger than the start? The path must pass through the × edges. Far smaller? Avoid them.

A ×2 or ×3 edge multiplies everything you did before it. Decide the multiplication edges first — which ones the path must use and where — then solve the small +/− adjustments around them. Two candidate paths through the same × edge differ only in cheap additions, which you can reconcile in your head.

When pruning leaves one candidate, run it forward a single time with left-to-right arithmetic before submitting — a wrong path counts as a miss and you re-solve the same maze. One forward pass costs two seconds; a miss costs ten.

Tier 1 mazes are two rows, +/− only — forward-trace them by eye and bank the points. Switch to backwards-first the moment the maze grows to five or six columns or shows a ×: that’s where forward tracing starts costing double-digit seconds and the pruning habits pay for themselves.