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Omni-MATH / Wendy eats sushi for lunch. She wants to eat six pieces of sushi arranged in a…

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problem

Wendy eats sushi for lunch. She wants to eat six pieces of sushi arranged in a 2×32 \times 3 rectangular grid, but sushi is sticky, and Wendy can only eat a piece if it is adjacent to (not counting diagonally) at most two other pieces. In how many orders can Wendy eat the six pieces of sushi, assuming that the pieces of sushi are distinguishable?
Plain-text mathematical notation (without MathML)
Wendy eats sushi for lunch. She wants to eat six pieces of sushi arranged in a 2×3 rectangular grid, but sushi is sticky, and Wendy can only eat a piece if it is adjacent to (not counting diagonally) at most two other pieces. In how many orders can Wendy eat the six pieces of sushi, assuming that the pieces of sushi are distinguishable?
Original LaTeX notation
Wendy eats sushi for lunch. She wants to eat six pieces of sushi arranged in a $2 \times 3$ rectangular grid, but sushi is sticky, and Wendy can only eat a piece if it is adjacent to (not counting diagonally) at most two other pieces. In how many orders can Wendy eat the six pieces of sushi, assuming that the pieces of sushi are distinguishable?

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