Henry Ernest Dudeney/Puzzles and Curious Problems/352 - Locating the Coins

Puzzles and Curious Problems by Henry Ernest Dudeney: $352$

Locating the Coins

Said Dora to her brother:

"Put a shilling in one of your pockets and a penny in the pocket in the opposite side.

Now the shilling represents $12$ and the penny $1$.

Triple the coin in your right pocket, and double that in your left pocket.

Add these products together and tell me whether the result is odd or even."

He said the result was even, and she immediately told him that the shilling was in the right pocket and the penny in the left one.

Every time he tried it she told him correctly how the coins were located.

How did she do it?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Unclassified Problems: $352$. -- Locating the Coins
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $254$. Locating the Coins