Maths mystery (2)

Anything goes, but keep it seemly...

Maths mystery (2)

Postby Cec » Sun Apr 30, 2006 11:25 am

Thought I'd post this.

My apologies for not presenting this "square" in a better way. It looks OK in my message box until I hit the "Preview" button. Suggestions for improved layout most welcome. Anyway here's the puzzle:

Known as the "Chinese Square" it requires the placement of only one of the digits 1 to 9 at each of the nine positions shown by a capital letter such that every row, every column and both diagonals add up to 15.

For example but not the correct placings, digit 5 placed at A, a 3 placed at D and a 7 placed at G would total the required 15 for column ADG.


A B C


D E F


G H I


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Re: Maths mystery (2)

Postby Smythe Dakota » Sun Apr 30, 2006 11:47 am

Cec wrote:.... It looks OK in my message box until I hit the "Preview" button. Suggestions for improved layout most welcome. ....

If you precede your tabular information with "[kode]" and follow it with "[/kode]", the system will (a) use a monospace font for better alignment, and (b) respect whatever number of spaces you insert between characters, or before the first character.

Spell it correctly, though ("code" not "kode") and don't use quotes. I had to misspell it above to prevent the system from interpreting it as an instruction.

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Postby udosuk » Sun Apr 30, 2006 12:17 pm

Actually, you can freely display [code] & [/code] by checking the "Disable BBCode in this post" option...

And Cec, your "problem" feels like an old commonly known one but you presented it so "mysteriously" that it sounds like something new... ^_^
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Postby Ruud » Sun Apr 30, 2006 1:00 pm

Code: Select all
ABC
DEF
GHI


This puzzle needs 2 clues to have a unique solution. As it stands, the puzzle has 8 solutions.

If you want to give it a try yourself, stop reading here.

Here is a list with all combinations that sum up to 15, per leading digit. The last 2 digits can be exchanged.
Code: Select all
1+14 159 168
2+13 249 258 267
3+12 348 357
4+11 429 438 456
5+10 519 528 537 546
6+ 9 618 627 645
7+ 8 726 735
8+ 7 816 825 834
9+ 6 915 924


E=5, because 5 is the only digit that can be used in 4 different combinations.
Code: Select all
...
.5.
...


For each corner, we need digits that can be used in 3 combinations.

2, 4, 6 & 8 must be placed in the corners (ACGI).

8 configurations possible:
Code: Select all
2.4
.5.
6.8

2.6
.5.
4.8

4.2
.5.
8.6

4.8
.5.
2.6

6.2
.5.
8.4

6.8
.5.
2.4

8.4
.5.
6.2

8.6
.5.
4.2


Remaining digits can now be placed in BDFH, leading to the following 8 solutions:

Code: Select all
294
753
618

276
951
438

492
357
816

438
951
276

672
159
834

618
753
294

834
159
672

816
357
492


For a unique solution, we need 2 clues that are not equal to 5 and no not sum up to 10.

Ruud.
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Maths Mystery(2)

Postby Cec » Sun Apr 30, 2006 4:01 pm

Thanks for all replies. I came across this puzzle in an old Reader's Digest "Book of Facts" which only gave one solution being this one:

492
357
816

Sorry to wind up but way past my bedtime (2AM) I'll read this thread again tomorrow including Bill's "Code" button suggestions to see where I'm going wrong.

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Postby Smythe Dakota » Sun Apr 30, 2006 5:21 pm

udosuk wrote:Actually, you can freely display [kode] & [/kode] by checking the "Disable BBCode in this post" option ....

Thanks for the tip -- I hadn't thought of that.

Of course, that would also disable [qwote] and [/qwote], so that trick isn't always available. In fact, I had to misspell "quote" here for just that reason (and I had to misspell "code" again, too). Or, I suppose I could have reversed them, putting [/quote] first and [quote] last (and similarly with [/code] and [code]), which would do the trick since they would no longer come in matching pairs.

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Postby Smythe Dakota » Sun Apr 30, 2006 5:24 pm

Hmm, it almost sounds as though we could make a whole new Sudoku (or some other kind of puzzle) out of this very feature. "Create a message having all of the following, in some order that will result in none of them being interpreted as instructions", or something like that, and then list a whole bunch of BBCode instructions.

:D

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Postby Ruud » Sun Apr 30, 2006 5:48 pm

There is a nifty little trick that allows you to show the tags without them being interpreted as BBCode.

Simply insert [b][/b] in the middle of the tag.

This will make [code[b][/b]]text[/code[b][/b]] look like [code]text[/code]

To prove I have enabled BBCode:
I wrote:you don't want to know what I had to write for that line:)


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Postby udosuk » Sun Apr 30, 2006 6:08 pm

Geez... How many more tricks do you have left up your sleeves Ruud? Or should I quote your name sized-up in gold+bold+italic+underline font like
Myself"][size=29][color=gold][b][i][u]The Incredible Ruud[/b][/i][/u][/color][/size][/quote] for this result:
[quote="Myself wrote:
The Incredible Ruud

:D

PS:
Any tricks for displaying the smiley emoticons and the ascii symbols at the same time? Of course you could use the code tags:
Code: Select all
:D :)
But I suspect Ruud has something more elegant...:)

And just confirmed code tags within code tags would go like this:
Code: Select all
[code][/code]


PS2:
Nevermind just figured it out... :D or should I type :[b][/b]D...:D
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Postby Smythe Dakota » Sun Apr 30, 2006 9:27 pm

Yikes! I had to pretend to reply with quote, just to see what on earth you were doing.

So now that I'm replying, I might as well go ahead and reply, I guess.

By the way, wouldn't [co[b][/b]de] work equally well?

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Postby udosuk » Mon May 01, 2006 3:31 am

Smythe Dakota wrote:Yikes! I had to pretend to reply with quote, just to see what on earth you were doing.

So now that I'm replying, I might as well go ahead and reply, I guess.

By the way, wouldn't [code] work equally well?

Bill Smythe


I see... You've disabled the BBCode in your last post, right? If you'd enabled it [code] would have been displayed instead...

If you wonder how I got this [code[b][/b]] up, I just typed that in: [code[b[b][/b]][/b[b][/b]]]...
Similarly to get [co[b][/b]de] you could have typed in [co[b[b][/b]][/b[b][/b]]de]...
But to display [co[b[b][/b]][/b[b][/b]]de] you'd need [co[b[b[b][/b]][/b[b][/b]]][/b[b[b][/b]][/b[b][/b]]]de]...:!:

Man I can't help myself... It's very catchy fun!:D :D
Last edited by udosuk on Mon May 01, 2006 11:52 am, edited 1 time in total.
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Maths Mystery (2)

Postby Cec » Mon May 01, 2006 5:09 am

Ruud wrote:For a unique solution, we need 2 clues that are not equal to 5 and no not sum up to 10

Am I right in concluding that your above criteria cannot occur for this puzzle in which case there is no unique solution. If that were the case then if someone produced any one of the eight solutions you came up with then I presume they would have to be credited with solving this puzzle?. Strangely, the Reader's Digest Book which showed just the one solution I mentioned above also stated the puzzle was thought to have originated about the 12th century BC. Well done on your deductions and explanations.

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Postby udosuk » Mon May 01, 2006 6:47 am

On a serious note, this subject matter is genuinely coming from ancient Chinese culture (though I don't eliminate the possibilities that other ancient civilizations might have touched on it independently)...

It's called "lo shu" or "luo shu" and was believed to have appeared on a turtle's back ~5000 years ago... You know how myths and fairytales go... But it's very believable that ancient Chinese mathematicians could have invented it out of curiosity or when studying astrology/numerology/fortune telling... The immensely interesting "I Ching" or "yi jing" ("Book of Changes") is enough evidence about ancient Chinese mathematical wisdom...

I'm sure what Ruud did was to demonstrate how everybody can solve this puzzle with the most basic algebraic knowledge, and was not claiming to having invented the solution process himself... I'm sure most Chinese kids would know how to solve this "puzzle" in primary grades...
Last edited by udosuk on Mon May 01, 2006 11:52 am, edited 1 time in total.
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Maths mystery (2)

Postby Cec » Mon May 01, 2006 1:04 pm

Thanks to the above suggestions I finally came up with this grid. However this was only achieved by a lot of fiddling with the space bar. What I've typed in the "Post a reply" message window box is different to this display (press the "Edit" button to view this). Is there any way to type the grid which produces an identical grid when the "Preview" button is selected to avoid the annoying process of fiddling with the space bar to eventually "get it right". Suggestions appreciated.
Code: Select all
 
A------B------C
|      |      |
|      |      |
|      |      |
D------E------F
|      |      |
|      |      |
|      |      |
G------H------J

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Postby Ruud » Mon May 01, 2006 2:00 pm

Cec wrote:Is there any way to type the grid which produces an identical grid when the "Preview" button is selected to avoid the annoying process of fiddling with the space bar to eventually "get it right". Suggestions appreciated.

I usually prepare these text in a fixed font editor, like Notepad.

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