Collect Gold Coins in LatticeVille

Benjie and Esther are exploring a mansion consisting of a \(5 \times 8\) grid of rooms. Each room contains a gold coin, but the explorers are only able to move North and/or East through the rooms, entering the room marked Start and leaving through the room marked End.

If Benjie and Esther take the paths shown, they will collect 22 coins. Can they collect more?

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