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

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

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?

If the answer is "even", the shilling is in the right pocket and the penny in the left.

If the answer is "odd", the shilling is in the left pocket and the penny in the right.

See Dudeney's Modern Puzzles from $1926$, no. $100$ - Odds and Evens, of which this a rehash.

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