Henry Ernest Dudeney/Modern Puzzles/180 - The Damaged Measure

by : $180$

 * The Damaged Measure
 * Here is a new puzzle that is interesting, and it reminds one, though it is really very different,
 * of the classical puzzle by concerning the weight that was broken in pieces
 * which would then allow of any weight in pounds being determined from one pound up to the total weight of all the pieces.


 * A young man has a yardstick from which $3$ inches have been broken off,
 * so that it is only $33$ inches in length.


 * Some of the graduation marks are also obliterated, so that only eight of these marks are legible;
 * yet he is able to measure any given number of inches from $1$ inch up to $33$ inches.
 * Where are these marks placed?


 * As an example, I give in the diagram the case of a $13$-inch rod with $4$ markings.


 * Dudeney-Modern-Puzzles-180.png


 * If I want to measure $4$ inches, I take $1$ and $3$; for $8$ inches, $6$ and $2$; for $10$ inches, $3$, $1$ and $6$; and so on.
 * Of course, the exact measure must be taken at once on the rod;
 * otherwise the single mark of $1$ inch repeated a sufficient number of times would measure any length, which would make the puzzle absurd.