Henry Ernest Dudeney/Modern Puzzles/142 - Economy in String/Solution

by : $142$

 * Economy in String

Solution
$2$ feet by $1$ foot by $\tfrac 2 3$ feet.

Proof
The total length of string that passes along the length, breadth or depth must in every case be the same to allow of the maximum dimensions, that is: $4$ feet.

The string passes $2$ times along length, $4$ times along breadth, and $6$ times along depth.

Therefore $4$ feet divided by $2$, $4$ and $6$ feet will give us $2$ feet, $1$ foot, and $\tfrac 2 3$ feet respectively for the length, breadth or depth of the largest possible parcel.