Henry Ernest Dudeney/Puzzles and Curious Problems/285 - The Teashop Check

by : $285$

 * The Teashop Check
 * We give an example of the check supposed to be used at certain popular teashops.
 * The waitress punches holes in the tickets to indicate the amount of the purchase.


 * $\boxed {\begin{array} {rcl} \\

\tfrac 1 2 \oldpence & --- & \bullet \\ 1 \oldpence & --- \\ 1 \tfrac 1 2 \oldpence & --- \\ 2 \oldpence & --- \\ 2 \tfrac 1 2 \oldpence & --- \\ 3 \oldpence & --- & \bullet \\ 4 \oldpence & --- \\ 6 \oldpence & --- \\ 7 \oldpence & --- \\ 8 \oldpence & --- \\ 1 \shillings & --- \\ & & \\ \end{array} }$


 * Thus, in the example, the two holes indicate that the customer has to pay $3 \tfrac 1 2 \oldpence$.


 * But the girl might, if she had chosen, have punched in any one of three other ways --
 * $2 \tfrac 1 2 \oldpence$ and $1 \oldpence$, or $2 \oldpence$ and $1 \tfrac 1 2 \oldpence$, or $2 \oldpence$, $1 \oldpence$ and $\tfrac 1 2 \oldpence$.


 * On one occasion a waitress said, "I can punch this ticket in any one of $10$ different ways, and no more."
 * Her coworker, whose customer owed a different amount, said, "Same here."


 * What were the amounts of the purchases of each of their customers?


 * Only one hole is allowed to be punched against any given amount.