Henry Ernest Dudeney/Puzzles and Curious Problems/36 - The Flagons of Wine

Puzzles and Curious Problems by Henry Ernest Dudeney: $36$

The Flagons of Wine

A quart of Burgundy costs $4 \shillings 9 \oldpence$, but $3 \oldpence$ is returnable on the empty flagon,

so that the Burgundy seems to be worth $4 \shillings 6 \oldpence$

For $12$ of the capsules with which each of the quart flagons is sealed, a free flagon of the same value is obtained.

What is the value of a single capsule?

Obviously a twelfth of $4 \shillings 6 \oldpence$ which is $4 \tfrac 1 2 \oldpence$

But the free flagon also has a capsule worth $4 \tfrac 1 2 \oldpence$, so that this full flagon appears to be worth $4 \shillings 10 \tfrac 1 2 \oldpence$,

which makes the capsule worth a twelfth of $4 \shillings 10 \tfrac 1 2 \oldpence$, or $4 \tfrac 7 8 \oldpence$,

and so on ad infinitum, with an ever-increasing value.

Where is the fallacy, and what is the real worth of a capsule?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Money Puzzles: $36$. -- The Flagons of Wine