Henry Ernest Dudeney/Modern Puzzles/190 - Packing Cigarettes

Modern Puzzles by Henry Ernest Dudeney: $190$

Packing Cigarettes

A manufacturer sends out his cigarettes in boxes of $160$;

they are packed in $8$ rows of $20$ each, and exactly fill the box.

Could he, by packing differently, get more cigarettes than $160$ into the box?

If so, what is the greatest number that he could add?

At first sight it sounds absurd to expect to get more cigarettes into a box that is already exactly filled,

but a moment's consideration should give you the key to the paradox.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Measuring, Weighing, and Packing Puzzles: $190$. -- Packing Cigarettes
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Geometrical Problems: Solid Geometry Puzzles: $326$. Packing Cigarettes