Twelve coins problem

[Mike L]

This is all a bit too difficult for my poor old brain. I haven't been able to come up with a solution, but I do have a comment on Dreams' solution:

Spoiler:

Dreams, you say that there are three coins in each bag. You end up by paying the miser one of the bags. But that implies that you are allowed to give the miser two good coins and one fake, without telling him which is the fake.

I read the original problem as saying that you can't pass a fake coin. You seem to be saying that it doesn't matter if the miser gets a fake, provided he also gets the two good coins to which he is entitled.

I guess that's fair enough. After all, the miser has the means to determine which is the fake.

A good solution. Well done.

And thanks to PDurrant for this interesting problem, even though I spent much too much time thinking about it.

[pdurrant]

Originally Posted by Mike L

This is all a bit too difficult for my poor old brain. I haven't been able to come up with a solution, but I do have a comment on Dreams' solution:

re: your comment. It's not permissible to use a fake coin to pay for something, but it's OK to give it to someone as a free gift.

[Mike L]

Originally Posted by pdurrant

re: your comment. It's not permissible to use a fake coin to pay for something, but it's OK to give it to someone as a free gift.

Ah, yes - especially if you don't stipulate that the recipient has to know that the free gift is a fake.

But wait, in that case .....

Spoiler:

Skip the weighing. Give any ten coins to the person you are buying the product from. At least nine of them will be genuine. The other is the free gift, which might or might not be genuine, but you've satisified your criteria.

And you'll end up with either one or two genuine coins to use another time, which you wouldn't have otherwise. Then, applying the same logic, you would be able to make another purchase which costs one coin.

Hmm ....

[pdurrant]

Originally Posted by Mike L

Ah, yes - especially if you don't stipulate that the recipient has to know that the free gift is a fake.

But wait, in that case .....

Spoiler:

Skip the weighing. Give any ten coins to the person you are buying the product from. At least nine of them will be genuine. The other is the free gift, which might or might not be genuine, but you've satisified your criteria.

And you'll end up with either one or two genuine coins to use another time, which you wouldn't have otherwise. Then, applying the same logic, you would be able to make another purchase which costs one coin.

Hmm ....

I think you've found a flaw in my puzzle.

The next problem for everyone - fix the question to remove the flaw!

[omk3]

There's no flaw. Only the miser has the means to identify the fake coin. No one else would accept it.

And you don't want to risk giving away a perfectly good coin, do you?

[Mike L]

On another point:

Why do we assume the person who owns the scales is a miser?

Should we not congratulate him on using his business acumen to corner the market in renting out weighing devices? There's obviously a market for his service, and he is offering it at a price that the market seems willing to pay.

Of course, if my solution to the puzzle is widely accepted, he will quickly go out of business. But that's OK too. We can't afford to support outdated industries whose services are no longer relevant.

It's all a nice little lesson in capitalism.

[LCF]

Originally Posted by omk3

There's no flaw. Only the miser has the means to identify the fake coin. No one else would accept it.

And you don't want to risk giving away a perfectly good coin, do you?

but give away two good coins,. just to be sure who gets the fake one? Unlike the (very good) answer you gave before, I fail to see the logic here

[omk3]

Well, when you pay the miser, you don't give the coins away, you pay for a service.
Sure, it's cheaper to give one away than buy a service for two, but, erm...it's the principle of the thing?

It's really fun criticising logic puzzles from a socioeconomic point of view

[LCF]

You have a point there - economy needs support - especially in such difficult times. Ok, guys, let's make it easier for you - I have a digital scale(s?) and charge 1 coin for 3 weights. (I think that's called free market or something similar, definitely having nothing to do with the word dumping )

[pdurrant]

Originally Posted by LCF

You have a point there - economy needs support - especially in such difficult times. Ok, guys, let's make it easier for you - I have a digital scale(s?) and charge 1 coin for 3 weights. (I think that's called free market or something similar, definitely having nothing to do with the word dumping )

Now that's the start of a whole new 'find the fake coin(s)' problem. What if we're using digital scales that will give a weight in grams, but doesn't directly compare two things?

Now, one coin for three weighings is better value than one coin for one comparison, but not by as much as it seems...

[LCF]

and yet, you could locate enough real coins with 3 digital weighings to pay he first item. Now, paying me is going to be a hazard or you get another 3 , pay me with 2 real coins and keep the fake as a souvenir

[pdurrant]

Next puzzle is up: https://www.mobileread.com/forums/showthread.php?t=88107