Henry Ernest Dudeney/Modern Puzzles/8 - Buying Buns/Mistake

Source Work

 * Arithmetical and Algebraical Problems
 * Money Puzzles
 * $8$ -- Buying Buns
 * $8$ -- Buying Buns

Mistake

 * Buns were being sold at three prices:
 * one a penny,
 * two a penny,
 * and three a penny.
 * Some children (there were as many boys as girls) were given sevenpence to spend on these buns, each receiving exactly alike.


 * How many buns did each receive?


 * Of course no buns were divided.

The solution offered:


 * There must have been three boys and three girls,
 * each of whom received two buns at three a penny
 * and one bun at two a penny,
 * the cost of which would be exactly sevenpence.

There are in fact $12$ solutions.

The full analysis can be found here.