Henry Ernest Dudeney/Puzzles and Curious Problems/153 - A Military Puzzle/Solution

by : $153$

 * A Military Puzzle
 * An officer wished to form his men into $12$ rows, with $11$ men in every row,
 * so that he could place himself at a point that would be equidistant from every row.


 * ''"But there are only one hundred and twenty of us, sir," said one of the men.


 * Was it possible to carry out the order?

Solution
Place the men along the sides of a regular dodecahedron with the officer in its centre.

You will find that the men at the vertices of this dodecahedron will be in two rows of $11$ men at the same time.

Hence $120$ men are needed for this arrangement.