Henry Ernest Dudeney/Puzzles and Curious Problems/227 - A Match-Boarding Order

Puzzles and Curious Problems by Henry Ernest Dudeney: $227$

A Match-Boarding Order

A man gave an order for $297$ feet of match-boarding of usual width and thickness.

There were to be $16$ pieces, all measuring an exact number of feet -- no fractions of a foot.

He required $8$ pieces of the greatest length, the remaining pieces to be $1$ foot, $2$ feet, or $3$ feet shorter than the greatest length.

How was the order carried out?

Suppose that the eight of greatest length were $15$ feet long, then the others must be made of pieces $14$ Definition:Foot (Linear Measure)foot, $13$ foot or $12$ foot lengths,

though every one of those lengths need not be represented.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Geometrical Problems: Various Geometrical Puzzles: $227$. -- A Match-Boarding Order
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $242$. A Matchboarding Order