How many chocolates you get?

Question

Imagine, you have $6.59 dollars. You are going to buy chocolates for all of it. A chocolate costs 50 cents and also, the shopkeeper will give you 1 chocolate if you give him 2 chocolate covers then he will give you a chocolate for free. So now how much chocolate can you get?

Answer 1

Well, with $6.59, I can buy 13 chocolates (assuming no fractional chocolates are sold), with 9c left over.

Now I have 13 chocolates and have 13 wrappers, with which I can get 6 more chocolates.

Now I have 6 more chocolates and 7 wrappers (one wrapper left over from the 13)

Now I get 3 more chocolates and have 4 wrappers (one wrapper left over from the 7)

Now I get 2 chocolates and have two wrappers.

Now I get 1 chocolate and have one wrapper.

Assuming I cannot get 1/2 of a chocolate with that one wrapper, I have a total of 25 chocolates.

If fractions are allowed, I could get an additional chocolate with the one wrapper, but it would take an infinite number of transactions. Similarly, I could get an additional 9/25 of a chocolate with the 9c, if fractions are allowed.(Details on request)

Comments

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You're making me blush, Dan! 

Answer 2

Dear Dan,

Those ALL look good, so I will just take all you have plus everything that OtherTink has calculated also!

Comments

Virginia, won't you get a tummy ache if you eat all those at one sitting? 

Or were you planning to eat them over a more extended period of time? 

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Dear OtherTink,

The answers to your questions respectively are YES, and NO...

Actually, it is called a chocolate hangover...and I have had more of those than the regular kind of hangover...(sigh)...

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Dear Virginia,

I have a solution for you!   With these, you can enjoy both kinds of hangover at the same time! 

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omg, every day on the Internet you can discover something awesome and wonderful that TRULY makes life worth living!!!

Diverse hangovers...and look at the labels too, Jim Beam and Canadian Club oh isn't life sweet...

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@T(h)ink

Lol - wouldn't that be worse?

There is an organisation preventing from drunk driving, but the hangover of the next morning is another "challenge".

https://en.wikipedia.org/wiki/Op%C3%A9ration_Nez_rouge

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Marianne, I did not know about Operation Nez Rouge...what a wonderful idea he had! Are you in Canada, is that how you knew of the organization?

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@ Marianne:

Yes, of course the consequences would be worse, but the antecedents...

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@Virginia

Lol - no, I am not in Canada, but the "Opération Nez Rouge" is also popular in Europe, at least in the "francophone countries" (I am Swiss). 

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Well anyway, Marianne, I am VERY glad to learn about such a worthwhile project as Nez Rouge...

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@T(h)ink

Lol - the antecedents ? I think that you might have an interesting story to tell ...

 

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Ha ha, hi Marianne well yes I have drunk deeply of life, you might say...

Still as far as the alcohol, it's somewhat more talk than actual drinking. Early on, a sociologist friend told me that a love of chocolate could indicate a tendency toward alcoholism...and so I was always careful because that was NOT a road I wanted to go down! Still though, beautiful glasses, wonderful liquor and liqueurs...I like to have them on hand, just because they are so beautiful.

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@Virginia

Yes, it was an excellent idea; it is a bit strange that it did not spread more and occur more often ...

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@Virginia

You will laugh; yes, me too! I was/am not so keen on drinking alcohol, but appreciate(d) an exquisite "drop" at special occasions, or tasting a good wine or beer, from time to time. Yet, since I am driving, I prefer(red) to abstain from alcoholic drinks (and also, when on diet), as soon as I am using my car. On the other hand, I liked and still like gourmet food and chocolate, of course.

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One absolutely MUST sample the beautiful things of life, Marianne!

...and fine alcohol is a graceful and gracious delight not to be missed...(not to mention chocolate)

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@Virginia

I agree with you, Virginia.

Yes, there are lots of precious little moments, inspiring thoughts and delights; and the little pleasures are part of them - at the right dosis - lol.

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Answer 3

Lol - I am late - again.

I can only say: wow, brilliant!

There seems to be just a part of one chocolate left (if I remember well 50 % (wrap) + 18 % (9 cents), provided that the chocolates may be cut in pieces - well, still better than nothing.

Now, if one chocolate (perhaps a truffle?) weighs 20 g, 25 pieces would total 500 g - enough to cause a "chocolate hangover", if you are eating them all by yourself.

Some food specialists would recommend no more than 1 or 2 per day, for instance after lunch, with some tea or coffee, or with an apple or, perhaps, sharing them with family and best friends.

And if these chocolates contain already some fine alcohol, you'd better stick to reasonable doses - lol.

An example with the recipe:

http://www.taste.com.au/recipes/grand-marnier-chocolate-truffles/c1266b0d-8047-4668-9782-71e16f3b69f8

Comments

@ Marianne:

An excellent recipe!  The only problem is, I think I would eat all the ingredients as I prepared them, and there would be nothing left! 

Oh, and with the puzzle chocolates:  If you are left with 1 wrapper, and fractions are allowed, you could then use that wrapper to get 1/2 of a chocolate and 1/2 of a wrapper. That 1/2 wrapper would then get you 1/4 of a chocolate and 1/4 of a wrapper, and so on. So the total chocolate you would get from the initial 1 wrapper is 1/2 + 1/4 + 1/8 +1/16..., which totals to one whole chocolate in the limit of infinite transactions.

A similar calculation would give you 9/25 = 36% of a whole chocolate for the 9 cents.

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@T(h)ink

Lol - as far as you are equipped with a microscope and the adequate tools and equipments to cut the increasingly miniaturised parts of wrapper and chocolate into the accurate portions.

As to the recipe, yes, it is hard to resist while preparing them. Years ago, when I tried to make my own truffles for the first time: about 400 - 500 g (without alcohol) and took them the following day to work, for the coffee break (my colleagues knew that it was my first trial). That evening, when I went home, no single truffle was left, my colleagues loved them. I think that I had two in all - and I was happy about the success.

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Lol, the chocolate seller should just give the customer a whole chocolate (with no wrapper), to save himself a lot of time and a lot of cutting. 

And about your truffles:  I'm not surprised they were a big success, but sorry that you only got two of them.   

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Lol - I was not sorry, I had a very good conscience regarding the caloric issues. 

Actually, the "gift" or "additional discount" would have been the nicest idea.