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

by : $227$

 * 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 $14$ foot, $13$ foot or $12$ foot lengths,
 * though every one of those lengths need not be represented.