Christmas Puzzle

This is a logic puzzle I picked up some time back. I think a version appears in a great book called Modern Heuristics.

Warning – it’s a bit of a time waster. But there is a solution, I promise.

The Fake Coin

A man – let’s call him Chris – is walking in a small, little known back road of Bath. The night is dark and cold, snow is gently falling around him. He wraps his threadbare coat around him and trudges on, feeling the slush ooze through the holes in his boots.

Finally he reaches his destination, a disreputable looking shop. The sign ‘Antiques Dealer’ is dimly visible in the flickering light of the single fluorescent tube that indicates the shop is open. Chris enters, and almost to his surprise finds the shop occupied.

For standing behind the desk is the owner, an old man with shrewd eyes and a disconcerting manner of asking questions laden with hidden subtlety.

“Yes?” he asks, imbuing the syllable with infinite nuance. He glances briefly at Chris’ shoes and coat.

“Well” stumbles Chris. “I have some valuable coins”.

And indeed he does. From deep within the pockets of his ancient garb, he produces 12 identical coins of exquisite beauty. Each has a Christmas scene embossed on one face, while the other describes the coin’s worth in some exotic currency.

The old man spends some time examining the coins before turning to Chris.

“Well?” he asked, once again turning taciturnity to eloquence.

“..er…”, adds Chris. “The thing is, one of these coins is a fake”

“Indeed”. Chris is not sure if this is a question or a statement.

“It is only one” Chris goes on. “And it should be lighter than the others – ”

The merchant retrieves an ancient pair of scales from a dusty shelf.

“Three weighings” he tells Chris, with the obvious satisfaction of one who has done this kind of computation before.

“ – er – or heavier”.

The old man gazes at Chris.

“I mean, the man who gave them to me said the fake was a different weight, but didn’t tell me if it was lighter or heavier” he gabbles.

“You just can’t rely on some people”.

There is an uncomfortable pause as Chris considers to whom this remark applies.

The old man considers a moment.

“Do you need to know if it’s lighter or heavier?” Chris asks nervously

The man looks at him as if he is an imbecile and Chris has his answer.

“Still 3” he finally concludes with grim satisfaction.

CAN YOU FIGURE OUT WHICH IS THE FAKE COIN – AND WHETHER IT IS LIGHTER OR HEAVIER –  IN JUST 3 WEIGHINGS?

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