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Omni-MATH / Five people of heights 65,66,67,68, and 69 inches stand facing forwards in a line. How many orders are there for them to line up, if no person can stand immediately before or after…

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problem

Five people of heights 65,66,67,6865,66,67,68, and 69 inches stand facing forwards in a line. How many orders are there for them to line up, if no person can stand immediately before or after someone who is exactly 1 inch taller or exactly 1 inch shorter than himself?
Plain-text mathematical notation (without MathML)
Five people of heights 65,66,67,68, and 69 inches stand facing forwards in a line. How many orders are there for them to line up, if no person can stand immediately before or after someone who is exactly 1 inch taller or exactly 1 inch shorter than himself?
Original LaTeX notation
Five people of heights $65,66,67,68$, and 69 inches stand facing forwards in a line. How many orders are there for them to line up, if no person can stand immediately before or after someone who is exactly 1 inch taller or exactly 1 inch shorter than himself?

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