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

Puzzles and Curious Problems by Henry Ernest Dudeney: $285$

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.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Combination and Group Problems: $285$. -- The Teashop Check