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## #1 2013-05-22 22:10:20

phrontister
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### Chocolate!

Hi all,

Here is a YOB/YOP-type puzzle (some of you know what that means) that I'd forgotten about, and that stefy asked if I had any more of.

I found it some time ago on another forum (now closed) and solved it, but instead of posting my answer there I replied with a puzzle of my own, the solution to which proves I solved the Chocolate! puzzle. So for anyone to know that I'd solved it, they had to solve mine too (which no one ever did).

Chocolate!:

Jake and Marie are on their way to visit Grandma, who lives at the end of the valley. It's her birthday, and they have a basket with chocolate bars they bought to give her.

Between their house and Grandma's they have to cross 7 bridges, and (it goes without saying) there is a troll under every bridge! The trolls, quite rightly, insist they each be paid a 'troll toll' before Jake and Marie can cross their bridge, the toll being half the number of chocolate bars in the basket; but they're kind trolls, and each, in turn, returns a single chocolate bar to the basket.

How many chocolate bars do Jake and Marie leave home with to arrive at Grandma's with 2 chocolate bars?

My puzzle:

By ascribing a numeric value to the letters of "Jake", "Marie" and "troll" based on each letter's position in the alphabet (ie, a=1, b=2......z=26) and then adding them together, a value can be obtained for each name.

You will then find that the reverse of the difference between the numeric value of "troll" and the sum of the product of the digits of the numeric value of "Jake" and the product of the digits of the numeric value of "Marie", multiplied by the sum of the digits of the prime factors ("PF") of the afore-mentioned product sum, divided by the sum of the digits of the difference between the number comprising the PFs (arranged in ascending prime factor order) and its reverse, less the sum of twice one less than half the quotient and the two bars left over for Grandma, equals the total number of troll-toll chocolate bars.

So I guess the question is this:
Can you verify that I actually solved the Chocolate! puzzle?

EDIT 23/5/13: In 'My puzzle', replaced the two clauses after "and its reverse" (near the end) with "less the sum of twice one less than half the quotient and the two bars left over for Grandma"...to remove ambiguity.

Last edited by phrontister (2013-05-23 19:03:41)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

## #2 2013-05-22 22:31:47

anonimnystefy
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### Re: Chocolate!

Hi phro

Thanks for posting this!

For the first puzzle: When do the trolls return the chocolates?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #3 2013-05-22 22:34:33

ShivamS
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### Re: Chocolate!

It says "each, in turn" thus I presume that they return one chocolate bar immediately after taking the toll.

I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

## #4 2013-05-22 22:38:38

anonimnystefy
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### Re: Chocolate!

But, that just means they return them in the order they take them, not when.

I am asking because, if they return a chocolate immediately, I get a weird

.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #5 2013-05-22 22:43:39

ShivamS
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### Re: Chocolate!

Well yes, that seems too easy if they take one and return one.

I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

## #6 2013-05-22 22:45:35

anonimnystefy
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### Re: Chocolate!

Khm, you do mean take a half and return one, don't you?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #7 2013-05-22 22:53:09

phrontister
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### Re: Chocolate!

#### Shivamcoder3013 wrote:

It says "each, in turn" thus I presume that they return one chocolate bar immediately after taking the toll.

Correct. The first troll takes the entire toll required for their bridge, and then, because they're so kind, immediately returns one chocolate bar to the basket. Jake and Marie then move on to the next bridge, and the toll process is repeated...and so forth, until all bridges are crossed.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

## #8 2013-05-22 22:53:58

ShivamS
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### Re: Chocolate!

Yes, but assuming they start with 2, take one (half of two) and return one immediately. That probably is not the case.

I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

## #9 2013-05-22 23:02:22

anonimnystefy
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### Re: Chocolate!

It is good that the other puzzle is there as a check.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #10 2013-05-22 23:10:54

phrontister
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### Re: Chocolate!

Yes...for the same reason that I included the solution check in 'bobbym's YOB'.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

## #11 2013-05-23 00:28:13

anonimnystefy
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### Re: Chocolate!

Hi phro

Last edited by anonimnystefy (2013-05-23 01:16:48)

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #12 2013-05-23 02:12:34

phrontister
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### Re: Chocolate!

Hi stefy,

Spot on!

I corrected an error in the second line of the second paragraph in my first post, and also improved the wording of the "reduced to..." part of the puzzle to "reduced to the cube root of the sum of the digits of that division".

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

## #13 2013-05-23 03:34:28

anonimnystefy
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### Re: Chocolate!

The "reduced to..." part is still a bit ambiguous. At first I thought that what I need is x-cbrt(x).

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #14 2013-05-23 08:18:04

phrontister
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### Re: Chocolate!

I agree...which is why I amended the wording (particularly after seeing your first answer before your edit). It's always worried me a bit, but as I understood what I meant there I managed to convince myself that it was ok. I think I'll do something about that...it just needed someone like yourself to confirm my misgivings about it and to prompt me into action.

And maybe that's why my puzzle was never solved on that dead forum!

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

## #15 2013-05-23 08:23:21

anonimnystefy
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### Re: Chocolate!

Hi phro

Yeah, the wording needs a fix.

And, speaking of words, do you, maybe, remember those old girthbruins' threads about finding what's in common for a set of words?

Last edited by anonimnystefy (2013-05-23 08:34:05)

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #16 2013-05-23 08:38:35

phrontister
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### Re: Chocolate!

Yes, I do. They were excellent puzzles and I quite enjoyed them.

There was one puzzle (I forget which one now) that I didn't manage to solve, which bothered me for ages and I've tried many times since the thread died to try and solve it. Maybe I'll look at it again, now that you've raised its spectre.

Am getting ready for work, and really must go now...

Last edited by phrontister (2013-05-23 08:39:28)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

## #17 2013-05-23 08:44:31

anonimnystefy
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### Re: Chocolate!

The problem with those puzzles is I have no idea where to even start. I have never solved one, and I don't know where to find simpler ones.

See you later!

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #18 2013-05-23 19:02:22

phrontister
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### Re: Chocolate!

#### anonimnystefy wrote:

Yeah, the wording needs a fix.

Fixed. (see post #1)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

## #19 2013-05-23 22:13:50

anonimnystefy
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### Re: Chocolate!

But, the cube root version was fine. It just needed rewording.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #20 2013-05-24 00:35:09

phrontister
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### Re: Chocolate!

True, and I did a reword with that in it. But while I was at it I also thought up about 3 other alternatives for that ending (there are many, of course), none of which featured the cube root...and out of the lot (including the cube root version) the one I posted was my favourite.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

## #21 2013-05-24 00:41:57

anonimnystefy
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### Re: Chocolate!

I do not see "cube root" anywhere in the new puzzle...

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #22 2013-05-24 00:48:31

phrontister
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### Re: Chocolate!

The reword with the cube root in it was only in my head, composed while I was at work. I didn't write it down. So was the final version that I liked best, which I thought of while driving and recorded into my mobile via its sound recorder in case I forgot it.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

## #23 2013-05-24 01:57:32

anonimnystefy
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### Re: Chocolate!

Using a phone while driving?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #24 2013-05-24 02:17:20

phrontister
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### Re: Chocolate!

Well, it was a choice of either chancing to get an enormous fine or forgetting the fix...and I opted for the former, of course. Trying to write it down while driving would have been worse.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

## #25 2013-05-24 02:29:50

anonimnystefy
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### Re: Chocolate!

Now, that is a true puzzler!

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment