Joan's telephone number & my YOB

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Joan's telephone number & my YOB

Postby Surfertje » Tue Feb 24, 2009 12:20 am

Here is a puzzle that I had a lot of fun composing. As it suggests, the YOB section of Part B is best done with the help of a computer.

I've provided some helps, but if you'd rather do the puzzle without them just ignore the three formulas in blue and the prime factorization aids directly below them.
Joan's telephone number and my year of birth

Part A: Joan's telephone number
Joan said to Helen: "Will you ring me and let me know if you are able to come to the fête with me?"

"Gladly," said Helen, "but how will I remember your telephone number? I have no pencil with which to write it down, and I can seldom remember numbers."

"Well," said Joan, "maybe you can remember these four points about it, and work it out when you get home."

These are the four clues that Joan gave Helen:-
1. It consists of six digits, and no digit occurs more than once.
2. The product of the first three digits is equal to twice the product of the second three digits.
3. When added, the 1st, 3rd and 5th digits come to the same totals as do the 2nd, 4th and 6th.
4. The 1st digit is equal to the 3rd digit multiplied by the 6th.

What is Joan's telephone number?
Part B: My YOB
This part is based on Part A and contains some interesting nonsense, as well as a serious component by which you can ascertain my year of birth ("YOB") – which was in the 20th century AD – and Part A's year of publication ("YOP") – which my YOB predates.
That serious component can be solved longhand…IF you have LOTS of time to kill, have LOADS of paper, a new pen, TONS of stickability, can concentrate for HOURS on end, can factorize and want to try to prove that man can beat machine – but solving with the help of a computer is highly recommended. So don’t complain if you take the longhand route and run out of midnight were warned!:)

I used Excel for my solution, but…
1. Excel lacks digit-manipulation functions for three of the puzzle's tasks, so I used these formulas that I found on the internet:-
(a) To display a number's reverse: =SUM(VALUE(MID(A1,ROW(INDIRECT("1:"&LEN(A1))),1))*10^(ROW(INDIRECT("1:"&LEN(A1)))-1))
(b) To display a number's digit sum: =SUM(VALUE(MID(A1,ROW($A$1:OFFSET($A$1,LEN(A1)-1,0)),1)))
(c) To display a number's digit product: =PRODUCT(VALUE(MID(A1,ROW($A$1:OFFSET($A$1,LEN(A1)-1,0)),1)))
They are array formulas. Type them in as usual, left-click the formula bar & press CTRL+SHIFT+ENTER: Excel then encloses them in braces {}.
Cell "A1" contains the number you wish to manipulate. Change it suit your spreadsheet…but don't change "$A$1".
2. Excel lacks a prime factorization function. To factorize multiple numbers concurrently I adapted Dr. Kardi Teknomo's "Prime Factors Using Spreadsheet" program, found at
Here are image links to scaled-down versions of my two Excel worksheets, showing only the factorization component (including formulas):-
These helps may not work in non-Excel spreadsheets – 1(a) & 2 fail in OOoCalc – in which case some manual input may be required.

Now to the puzzle…

Joan's telephone number, by some extraordinary 'coincidence', yields the same answer, "X", for the sum of the telephone number's three left-to-right paired digits and for the sum of the three right-to-left pairings! (eg, telephone number "278960" gives 27+89+60 l-to-r and 06+98+72 r-to-l). Furthermore, X holds special significance because when it is divided by the square that remains after deducting my YOB from Part A's YOP (and also when the reverse of that specially-significant number, X, is divided by the square's reverse), the result is a prime number that is a factor of Joan's telephone number, and its reverse!!
Had Helen known that, working out Joan's telephone number would have been a snap!

A little-known fact that would have flipped the doily under Helen's plate of afternoon tea gateaux is that of the amazing link between Joan's telephone number, the letters in Helen's name and the letters in Joan's name. If a name's letters are ascribed a value corresponding to their position in the alphabet (ie, a=1, b=2......z=26), the sum of those values becomes the name's "numeric value"; and if we multiply the numeric values of Joan's and Helen's names together and divide the result by the sum of the number of digits that appear in Joan's telephone number and those that do not (and don't forget the zero!), we arrive at that same specially-significant number – you guessed it – X, again!!

An even lesser-known fact that would have popped Helen's tea cosy right off the teapot is that the product of the values of the letters in Helen's name, divided by the product of the values of the letters in Joan's name, multiplied by the same prime factor of Joan's telephone number that I mentioned earlier, is – you guessed it again – that increasingly-specially-significant number, X, yet again!!

Even furthermore still (and knowing this would have enabled Helen to work out the number in her sleep!), the reverse of the difference between the product of the digits of my YOB and the product of the digits of Part A's YOP, multiplied by the reverse of the sum of the digits of the prime factors ("PFs") of the sum of my YOB and Part A's YOP, divided by the reverse of the product of the digits of the sum of the digits of the division of the difference between the number comprising the PFs (arranged in descending prime factor order) and its reverse by the sum of the digits of that difference, less a power of a root of the sum of the digits of the PFs, equals the sum of the digits not appearing in Joan's telephone number!!

What is my YOB and Part A's YOP? And what is the next solution each side of those years? All solutions are in the year range 0 to 3000 AD.

Solution check
The difference between the numeric value of Joan's name and the reverse of the division of the difference between the sum of the three YOB solutions and the sum of their digits by that "specially-significant number", X, equals the sum of the digits in Joan's telephone number.

1. Prime factors (PFs) include all repeat factors:-
eg, 1926 factorizes into 2x3^2x107: ie, 2x3x3x107…which, "arranged in descending prime factor order", becomes 107332.
2. Power and root exponents, and quotients, are positive integers.
3. The result of "the difference between" is an absolute value.

Here is a link to a .pdf file of the above:

Hope you'll enjoy it!:)


EDITS: (a) The first 13 relate to the original puzzle; (b) #14 = puzzle replaced with new version.
Last edited by Surfertje on Tue May 12, 2009 7:28 am, edited 14 times in total.
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Postby Smythe Dakota » Thu Feb 26, 2009 12:09 pm

Apparently you scanned in your puzzle from a hard copy. As a result, it took f-o-r-e-v-e-r to load. If you'd retype it as text, you might have more takers.

Bill Smythe
Smythe Dakota
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Postby Surfertje » Thu Feb 26, 2009 4:26 pm

Thanks for letting me know, Bill - I rarely post images on forums and I was unaware of this type of problem.

The image loads in 3-4 seconds for me (I've got high speed broadband), but it's a huge file size in .jpeg format and so I've changed it to .png, which shrank it down enormously (quality didn't change much).

I've edited my first post, and hopefully that will solve the download speed problem as I'd like to keep the formatting if I can. The original image was just a .jpeg screen capture of my MS Word page, and I'd saved it in the highest resolution for best display.

I've changed the other two images of my first post to .png too.

Last edited by Surfertje on Sat Feb 28, 2009 2:05 pm, edited 1 time in total.
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Postby udosuk » Thu Feb 26, 2009 5:55 pm

Surfertje wrote:The image loads in 3-4 seconds for me (I've got high speed broadband), but it's a huge file size in jpeg format and so I've changed it to png, which shrank it down enormously (quality didn't change much).

But the main file (Joanstelephonenumber.png) is now 1.6MB, even bigger than the original .jpg file (1.0MB).:!:

You're right that .png compress screenshot images much better than the .jpg format, but if you load a .jpg file first and then resave it to the .png format, the end result will be even worse.:idea:

The correct method to do it is to set up the original screen (e.g. open the word file), then copy the screenshot by pressing the "PrtSc" button on your keyboard, then paste the image to a program such as "Paint", then directly save it to the .png format. It should be a file around 100-200kB at most.

And you can even make it much smaller if you first save it to 256-color .bmp format, then resave it to .png format. But the quality will be a little rough (just a little). If you use 16-color .bmp instead it will shrink the file even further but I think the quality is not good enough.

Of course, if you use an alternative image editing program (don't ask me for any suggestion) which has the "palette optimization" feature, the result will be shockingly great (we're talking about <10kB here, and without any noticeable quality tradeoff too). But that's perhaps too much fuss.

But the question in the first place is why don't you just open the .doc file, copy and paste all the text and post in the forum directly. I would have done it for you, but it's my personal policy that I don't open .doc files created by other people on my personal PC (mostly because of the vulnerablity of Microsoft formats against malwares). That's why I don't recommend people sharing .doc, .xls files etc on the web, unless absolutely necessary and for business purposes.

I will try to solve the actual problems later.:)
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Postby Surfertje » Thu Feb 26, 2009 11:28 pm

udosuk wrote:...but if you load a .jpg file first and then resave it to the .png format, the end result will be even worse.:idea:

This is how I created that png file:-
I used SnagIt to screen-capture the .doc file by choosing the "Scrolling window" option. SnagIt has "palette optimization", and I chose 24-Bit, saving it directly as a tiny 108KB .png file. I then uploaded that same file to PhotoBucket, which (unbeknown to me) blew the size out to 1.6MB(!!) - as you said. I checked my PhotoBucket default sizes and also their help files, but I can't figure out what happened...and happened again when I retried it.:(

If others experience the same slow download as Bill did (although I didn't - even after clearing my temporary internet files), I guess that it's best to delete the puzzle image and replace it with the .doc contents - which I've just done by editing my original post. In case it might help someone there's also a link to a .pdf file of the puzzle, replacing the previous .doc link.

I'm sorry, but I hadn't properly considered the security issue of sharing .doc & .xls files. Unfortunately my biggest hint involves downloading the .xls file that contains my adaptation of Kardi Teknomo's single-number factorization program. Mine can factorize many numbers concurrently, enabling automated input of the results into each year-row of the main calculation worksheet, thus automating the checking of selected years in one fell swoop - which is quite an interesting and time-saving feature.

Maybe there are other ways of achieving a similar automated result (a prime-factorization function would have been nice - is there one?), but this is all I could come up with. So that leaves manual input...which, by the way, is how I initially constructed the puzzle - buried in my armchair with my calculator till very late at night! Later, I used Excel to refine it. Manual input of the prime factors will take a lot longer than using my automated process, of course, but for a realistic year-range it's still very doable.

Is there an acceptable way of sharing Excel worksheets on forums? Showing formulas instead of values in cells seems a bit cumbersome because of formula length (some are quite longish). Anyway, even if it's too hard to share my worksheets over a forum, working on that automated option was a challenging and fun exercise.:)

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Postby udosuk » Fri Feb 27, 2009 7:20 am

Thanks for the (re)editing.:)

I don't know about PhotoBucket much, but the 2 image hosting websites I use (imageshack and tinypic) allow us to upload .png files without changing their sizes at all, so I haven't experienced your problem.

As for security issues and such, it's just my personal preference that I don't like sharing MS Office files for recreational purposes, but I certainly can't speak for others, so just feel free to post them as you feel necessary. The fact that I won't use them doesn't mean others wouldn't.:)

Or perhaps you can consider posting your spreadsheet contents in the format of .csv files, which are practically text files using commas to separate the cell contents.:idea:

As for factorization and such, I don't know about others, but I always prefer to use my own programming/spreadsheet skills to work them out instead of relying on a program provided by someone else.:)

Thanks again, but I'm still too busy to start working on your puzzles. Hopefully others will show more interest soon.
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Postby Surfertje » Sat Feb 28, 2009 5:54 pm

Thanks for all your advice, udosuk - much appreciated.:)

udosuk wrote:As for factorization and such, I don't know about others, but I always prefer to use my own programming/spreadsheet skills to work them out instead of relying on a program provided by someone else.

Yes - that's so much more satisfying. I provided the factorization links because, outside of this forum, I've had zero success in interesting anybody in my puzzle so far - other than 3 people who solved Part A, with one of them going on to solve part of the 'nonsense' component of Part B. Although I've done my best with some obfuscation to blur the obvious, I didn't want to put people off entirely. Hence also the formula hints.

My main reason for the automated factorization for a range of numbers was to have an easy method of determining how close any other solutions were to the one I had in mind. There were several that were annoyingly close, but after I eliminated them with a couple of tweaks of that last paragraph, there's now only one solution for the years 0 to 4087 (ie, if my spreadsheet solution is correct). No doubt someone will want to be the first to find the next solution date, so I might have to renege that last comment in Note a hurry! ;)

So far only one person has downloaded my .xls file, so maybe others are busy working out their own too:!:
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Postby Surfertje » Sat Mar 07, 2009 9:03 am

I've just discovered that two of the hints - #1(a) & #2 - don't work in OOoCalc (but they work fine in MS Excel).:(

Unfortunately I don't have enough spreadsheet knowledge to correct that situation and so I've included an 'EDIT' note to that effect after the second paragraph in my first post.

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Postby Surfertje » Sat Mar 28, 2009 6:35 pm

I've changed "quadruple" to "square" in Part B's paragraph that begins "Joan's telephone number", as I had an incorrect understanding of the word "quadruple", thinking that it meant "4th power". The alteration should eliminate any confusion about it.

I came to that incorrect understanding from doing crossnumber puzzles, where "square", "cube" and "quadruple" are commonly used to denote 2nd, 3rd and 4th powers, but I've since found out that official names only exist for the 2nd and 3rd powers! :shock:

The change makes no difference to my intended answer in that section. Hopefully no one's wasted any time because of this hiccup!
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Postby Surfertje » Tue May 12, 2009 11:49 am

I've recently revised the puzzle and there's now a new version. Most of it remains unchanged and so I've simply edited the one in my first post.

I've never been completely happy with the phrase "(arranged in ascending prime factor order)" in the tricky "Even furthermore still" paragraph, because my spreadsheet's factorizing program automatically places the prime factors in ascending order and no arranging/rearranging has to be done. Therefore I've changed "ascending" to "descending".

For some added interest I've also included a "Solution check", happily managing to weave into it some other elements from earlier parts of the puzzle.

These changes necessitated some small alterations to that tricky paragraph...and not all solutions are the same as before.

Hopefully these changes are improvements!:)
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Postby udosuk » Mon May 18, 2009 2:07 pm

Hi Surfertje, the forum is just recovering (temporarily) from the terrible spam bombing during the past week. But rest assured your updating hasn't gone unnoticed. I'll look back at it later when I have more leisure time. Good on you mate!:)
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Postby Surfertje » Mon May 18, 2009 3:42 pm

Thanks for that update, udosuk. It's nice to know that you're still maintaining some interest in the puzzle - which hasn't exactly prompted fierce discussion to date. I guess the puzzle's a bit long - it would probably take more than an idle coffee break or two just to read the clues, let alone solve it.

I've had some good discussions lately with someone who solved it, and that led to this latest revision. I'm particularly pleased with the addition of the "Solution check" that also includes the "specially-significant" number, X, which, after its initial usage flurry, was then left neglected on the shelf. Same with the numeric value of Joan's name..

That spam bombing was rather worrying, as I witnessed Henk Westhuis's IntoSudoku forum being destroyed by spammers a couple of years ago. Henk had an excellent instructive Sudoku solver (freeware, still available for download), and the forum was quite active too. Then the floods came and washed it all away!:(
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