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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,606

I found this tricky puzzle on the internet.

Enjoy!

*PS...If the image doesn't display (which may happen, because it was uploaded under the old MIF system) click on the hidebox (I've tried to delete the old image, but can't):*

*Last edited by phrontister (2017-02-27 18:37:26)*

"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

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi phrontister;

How are you supposed to start these?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,606

Hi Bobby,

How are you supposed to start these?

Cross-number puzzles are number logic puzzles with clues/answers linked to each other, and it is up to the solver to work out which of them are so closely linked, and in which way, that something meaningful can be learnt from their association.

In the Introduction to his "Number Chains" book, Geoffrey R. Marnell writes:

"The clues, though, are not esoterically mathematical - you don't need any special mathematical training to solve them. You will, however, need to apply a little logic, for most clues do not yield the answer on their own but depend on the answer to another clue, itself dependent on the answer to a further clue, and so on.

You will sometimes need to eliminate possible solutions by trial and error, to run with possibilities until some - maybe many - steps later you discover which fit and which lead to contradiction or absurdity...

...the logic required is uncomplicated and the arithmetic simple. But if you think it's going to be easy, think again!"

Geoffrey R. Marnell's understanding of "a little logic" and "the logic required is uncomplicated" certainly differs from my understanding of them. He has a doctorate and is a Mensa member, whose puzzles have appeared in magazines and newspapers throughout the world.

As I see it, the *Little Pigley Farm* puzzle that I posted fits Marnell's description better than *NOHOW*, for which I used a little BASIC programming and some Excel to speed things up.

*EDIT: I've since got Excel to do the part that I programmed in BASIC.*

All I've ever needed for Marnell's puzzles and *LPF *are a calculator, a list of squares, cubes, quadruples and primes, paper, pen and a calculator...and some midnight oil! They're not easy!! But they are *very *satisfying to complete.

I still remember the feeling I got when I solved my first cross-number puzzle - which had done the rounds with my friends and was deemed to be too hard. It's easier than the two I've posted...maybe I should have started with that one, but I thought the members here would prefer something tougher. I might post it later, if *Little Pigley *and *NOHOW *go nowhere.

LG Horsefield in his "Cross-figure Puzzles" book gives some examples of strategy in a "Hints and Helps" section, but they're *very *simple. I could scan them and post the images if you like.

*NOHOW *is in a bit of a class and style of its own, as are other puzzles by Rhombus. Just making sense of the odd wording and working out what on earth he was getting at took me a while...but then I'm not the sharpest tool in the shed.

*Last edited by phrontister (2009-09-15 23:15:50)*

"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

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi phrontister;

Thanks for the info.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,606

Hi Bobby,

I found *NOHOW *particularly difficult to get started. It took forever before I could enter even one solved digit onto the grid, and until then I wondered if I was ever going to make any progress with it at all!

Perhaps you, or someone else here, can come up with a better strategy than mine (which wasn't a terribly logical one) - but I don't want to divulge what mine was yet. Without Excel's help I'd find the puzzle very time-consuming, as I haven't worked out a good logical strategy yet.

Horsefield says of his puzzles (which I'd class as being of medium difficulty):

"Ordinary people find that each puzzle occupies an hour or two - some more, some less."

Marnell says:

"They can be solved on the 8.23 to the office without a separate seat reserved for the

Complete Oxford Dictionary, a world gazetteer, a short history of the world and a dictionary of anagrams (the minimum library needed, it sometimes seems, to solve a cryptic crossword). Here is a type of puzzle everyone can finish, for innate logic is the key to its solution."

A Marnell puzzle can take a good puzzler *hours *to solve!

*Little Pigley* and *Mathematical Maelstroms* (I mentioned them in the *Little Pigley *post) fall somewhere in between Horsefield's and Marnell's puzzles, while the unusual *NOHOW *may be in a category of its own.

That's probably put everybody right off trying them!

*Last edited by phrontister (2009-09-15 23:21:49)*

"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

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,606

Hi,

For anyone wanting to use Excel to help them with this puzzle, here's a prime factorization function:

Excel doesn't have one, so it has to be added into Excel as a udf. Factors are output in a comma-delimited string in ascending order and contain repeat factors, if any. There's an option for the output to be in descending factor order, but that shouldn't be needed in this puzzle (it was specifically written into the function for another puzzle I posted earlier on that required that output order).

For all other formulas in my spreadsheet I used Excel's standard built-in functions.

Btw, I don't know that it's necessary to use a spreadsheet (or programming?) to help solve the puzzle, and quite possibly the puzzle's author intended a more logical and manual approach - but I can't find it and so resorted to using Excel.

But that was good too, because I like using Excel and things like this help me to get to know it better.

*Last edited by phrontister (2017-02-26 00:49:06)*

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,606

Hi Bobby,

How are you supposed to start these?

Sorry, Bobby...I wanted to be more helpful than I've been so far, but I didn't know how to do that and at the same time not spoil the puzzle.

William Y. Sit, who I think eats cross-number puzzles for breakfast, says this about NOHOW:

Formula: If x is a 3-digit number d3d2d1, let g(x) be the 5-digit number d30d20d1 (obtained by inserting two 0s between the digits).

The eleven clues have the form g(x) = y, where x is always just some 3-digit answer, but g(x) is a product of two 3-digit primes p and q, and y is an arithmetic expression involving only up to 2 answer variables.

That probably makes more sense to you than it does to me (it didn't help me one scrap), but in case it doesn't here's a MUCH bigger hint (I can't think of a smaller one that helps at all):

*Last edited by phrontister (2009-11-16 19:28:34)*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi phrontister;

I read that by Sit. Haven't looked at the great big hint yet, but I haven't filled in a single box yet. What dumbfounds me is say small b, it's a small letter so that means its down not across and because of the bold line do I have to stop at the 3rd box down?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,606

Hi Bobby,

I haven't filled in a single box yet.

I didn't fill in a single box for a *very *long time! Working out a solution strategy wasn't easy, as this puzzle is quite different from the cross-number puzzles I'm used to.

...small b, it's a small letter so that means its down not across

Yes...lower case letters are *down *clues and upper case are *across*.

...because of the bold line do I have to stop at the 3rd box down?

Yes. The answer to "b" is a 3-digit number filling the first three squares of the third column. The bold lines have the same function as the black squares in a normal crossword puzzle: ie, they denote the termination point of each clue solution.

*Last edited by phrontister (2009-09-21 02:08:42)*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi phrontister;

Thanks for much clarification.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,606

Hi Bobby,

While I was whiling away the hours in my time machine last night on that fruitless return journey with the plastic cheese, I had another go at solving this puzzle to see if I could find a solution strategy that was simple enough to do longhand. Nope - Excel was the only way forward for me.

I didn't mention this in the "Great big hint", but in the exercise there I used the *Factors* function that I gave a link to in an earlier post:

.

I don't know why something like this isn't included in Excel as standard equipment!

*Last edited by phrontister (2017-02-26 00:50:14)*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi phrontister;

You have provided enough, I am having fun spending a little time each day on it. I am getting nowhere but enjoying the play.

Sorry about the plastic cheese but it is my nature. Anyway, MathsisFun keeps interfering with my plans for domination of the cheese. He will have to be neutralized. Perhaps a joint effort can accomplish the task efficiently. We could then share the cheese.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,606

Hi Bobby,

Perhaps a joint effort can accomplish the task efficiently. We could then share the cheese.

That may not end well. I tried a similar thing once when playing *Risk 2210 AD.* One of the players (previously a good friend of mine) and I formed an alliance and were blasting the opposition out of the game, when one of us (I won't say who) saw an opportunity to break the union and so win the game.

The resulting cold war and stony silence is now thawing, and we've progressed beyond monosyllabic 'conversations'.

*Last edited by phrontister (2009-09-29 20:23:14)*

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,606

Hi Bobby,

I am having fun spending a little time each day on it. I am getting nowhere but enjoying the play.

I don't know if you're still having a crack at this, but NOHOW doesn't really seem to have hit the spot on MIF.

I'd like to try to get some discussion going about it to see others' strategies and if they differ from mine - which they probably will. I used modern tools to help with my solution of this 1966 puzzle and I doubt that I followed the author's intended strategy.

I'm thinking of posting it on a couple of other puzzle sites and in readiness for that I've deleted the great big hint I gave earlier. It really was far too great big a hint because it leads to a solution too obviously, thus influencing any thoughts on developing a strategy and consequently diminishing solving satisfaction.

Finding a way to make a solid start with this frustrating puzzle was, for me, half the fun, and I don't want to spoil it for others.

IMHTBO, NOHOW's a *terrific *puzzle. It only needs basic high school maths knowledge, but I found it to be a very enjoyable and satisfying teaser. A good calculator would come in handy, and certain components of the puzzle are very suited to using modern computing aids.

Do you know of any puzzle sites where this type of puzzle, and also two of my other unpopular puzzles - *Little Pigley Farm* and *Joan's telephone number & my YOB* - might get more acceptance?

*Last edited by phrontister (2009-11-17 09:25:02)*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi phrontister;

Long time no see. Glad your back! Sorry, that I couldn't do better with them myself. Hope you didn't stay away because you couldn't generate any general interest in the puzzles. That happens. I looked at them and didn't do well at all. You are way ahead of me and perhaps you could take the time to post your methods of solution. Your thoughts and feelings would be of interest to me. Anyway, welcome back!

P.S. But leave the second part of Joans telephone number unanswered.

Also you must clarify IMHTBO.

*Last edited by bobbym (2009-11-17 19:20:22)*

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,606

Hi Bobby,

Thanks for your welcome back! I've been away for a month and couldn't post...and it's good to be back.

I would have liked to have seen more interest in my puzzles here, but never mind...I'm quite happy participating on some of the other forums too. Unfortunately most of the maths topics are too advanced for me, otherwise I'd love to contribute more. I read a lot of the posts, but most of them just sail way over my head.

P.S. But leave the second part of Joans telephone number unanswered.

Many have tried and not succeeded in getting me to divulge any information that might help them progress with that part. Why should it be any different for you?! When I composed that bit of the puzzle I was feeling very mean...and nothing has changed.

Also you must clarify IMHTBO.

"In my humble though biased opinion". The bias refers to the pleasure I got from using Excel for my solution and learning some manoeuvres new to me...something that may not appeal to all. You weren't to know.

*Last edited by phrontister (2013-05-21 14:01:08)*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi phrontister;

I would have liked to have seen more interest in my puzzles here, but never mind...

Lots of my stuff doesn't engender any interest either. Heck, no one in here even talks to me except for MathsisFun and you.

I'm quite happy participating on some of the other forums too. Unfortunately most of the maths topics are too advanced for me, otherwise I'd love to contribute more. I read a lot of the posts, but most of them just sail way over my head.

When confronted with something baffling just ask the poster for a little bit more. Or ask me. I will do the best I can.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,606

bobbym wrote:

Heck, no one in here even talks to me except for MathsisFun and you.

Don't let Tigeree hear you say that, Bobby!

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi phrontister;

The women on this forum want me eviscerated. Or maybe, just drawn and quartered. Or perhaps my mouth sewn shut and packed with brine. '

I guess I still have the charm.

*Last edited by bobbym (2009-11-18 12:17:45)*

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,606

bobbym wrote:

I guess I still have the charm.

I think your avatar does it for you, Bobby (I don't know what else would).

*Last edited by phrontister (2013-05-21 14:02:04)*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi phrontister;

I think your avatar does it for you, Bobby

The avatar was given to me by MathsisFun.

http://www.mathisfunforum.com/viewtopic.php?id=13077

(I don't know what else would).

''

Glad you are getting a little feedback on your problem.

*Last edited by bobbym (2009-11-19 20:25:27)*

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,606

Hi!

I thought I'd raise this old puzzle back up to the surface, as I've just finished solving it (again) and enjoyed it so much I didn't want to keep it all to myself.

As before, I tried to find a non-CAS (other than calculator) solution, and, as before, failed in my attempt.

I think I'll give up looking for it, although I'm sure one must exist, given the fact that the puzzle was published way back in 1966.

Anyway, this time I've kept a good record of my solution method, which I hadn't done very well before.

If there's someone who's interested in solving this but is stuck and would like a hint, I'll try to come up with one that doesn't give the game away...unlike the 'great big hint' that I gave (since removed) in post #7. I've never seen the author's answer or solution technique, so the hint will relate to my method.

*Last edited by phrontister (2015-05-25 13:52:08)*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

As before, I tried to find a non-CAS (other than calculator) solution, and, as before, failed in my attempt.

Hmm, I am still trying to find a CAS solution.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,606

Not daily since September, 2009, surely!?

bobbym wrote:

I am having fun spending a little time each day on it. I am getting nowhere but enjoying the play.

Thinking of the old non-CAS brigade, it always staggers me when I consider how well they must have understood their maths, and how much they achieved without modern-day tools! >phew!< I have a collection of puzzles by Rhombus, all of which were created pre-modern CAS, and the ones I've tried are all supremely difficult! (for me).

I'm pretty pleased I've tackled this puzzle again, because I've streamlined my solution with better logic and improved several formulas. It's now nicely set out on my spreadsheet and makes much better sense than the mess I had before.

*Last edited by phrontister (2015-05-26 02:00:09)*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Nope, I can not even find my notebook on this. I did not get very far so I probably will be able to recreate it.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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