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Recreational Maths
http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=17&t=21		 Page 1 of 2
Author:  udosuk [ Tue Apr 29, 2008 5:00 pm ]
Post subject:  Recreational Maths
I like this section and I'm sure many members here are interested in recreational maths too. I mean does the name "Martin Gardner" ring a bell for anyone here? :geek:

Anyway, let me start a discussion here: who knows what my avatar (the pattern of numbers) is all about? :?:
Author:  Nasenbaer [ Tue Apr 29, 2008 7:50 pm ]
Post subject:  Re: Recreational Maths
Sorry, Martin Gardner didn't ring a bell.

But the horizontals and diagonals in your avatar all add up to 38. It seems like a special form of a magic square. Or did you mean something else?

Cheers,
Nasenbaer
Author:  rcbroughton [ Tue Apr 29, 2008 8:20 pm ]
Post subject:  Re: Recreational Maths
One of my very favourite Mathematical puzzles is one that my father showed to me about 20 years ago - and it was old, even then.

If you haven't come across it before, it's a real gem. It just doens't look like you have enough information to make any headway but very rewarding when you crack it.

Image

Code:
Across
1   Area in square yards of the Paddock
5   Age of Martha, Squire Root’s aunt
6   Difference in yards between the length and the breadth of the Paddock
7   Number of Roods in the Paddock times 8 down
8   The year the Root family acquired the Paddock
10   Squire Root’s age
11   Year of Mary’s birth
14   Perimeter in yards of the Paddock
15   Cube of Squire Root’s walking speed
16   15 across minus 9 down


Down
1   Value in shillings per rood of the Paddock
2   Square of the age of  Squire Root’s mother-in-law
3   Age of Mary, Squire Root’s daughter
4   Value in pounds of the Paddock
6   Age of Ted, Squire Root’s son, who will be twice the age of his sister, Mary in 1945
7   Square of the breadth of the Paddock
8   Time in minutes it takes Squire Root to walk 11/3 times around the Paddock
9   10 down divided by 10 across
10   10 across multiplied by 9 down
12   Sum of the digits of 10 down plus 1
Number of years the paddock has been in the Root family


Useful Information
The Paddock is a rectangular plot of land
The year is 1939
1 acre = 4840 square yards = 4 roods
1 mile = 1760 yards
1 pound = 20 shillings
Author:  Sublue [ Wed Apr 30, 2008 12:57 am ]
Post subject:  Re: Recreational Maths
Ding, ding, ding!!!
Martin Gardner definitely rings a bell with me. He was the topic of a number of discussions when I was working on my first Bachelor of Science degree (in Secondary Math Education). I have been wondering about your avatar, but hadn't gotten around to asking yet.
Susan
Author:  udosuk [ Wed Apr 30, 2008 1:43 am ]
Post subject:  Re: Recreational Maths
Nasenbaer wrote:
But the horizontals and diagonals in your avatar all add up to 38. It seems like a special form of a magic square. Or did you mean something else?

Yep, you got the right idea, only the wrong shape. :ok:

:arrow: http://en.wikipedia.org/wiki/Magic_hexagon

What if I tell you this pattern is the only essentially unique (normal) magic hexagon of a size larger than 1? Of the trillions of hexagonal pattern of numbers, only this pattern and the trivial single 1 stand as (normal) magic hexagons. Which makes it a million times more magical than any magic square you can imagine. :ugeek:

:arrow: http://en.wikipedia.org/wiki/Martin_Gardner

Martin Gardner is like the godfather of modern recreational maths (to the Western world at least). His books/columns/articles are treasure chests to anyone interested in playing with maths. His impact is only matched by the late Nob Yoshigahara to the modern Japanese world of puzzles. But I don't expect you guys to know much about "the great Nob". :alien:

Richard, interesting cross-number puzzle. :thumbs: Will take some time to work on it though. :study:
Author:  udosuk [ Fri May 23, 2008 5:07 pm ]
Post subject:  Re: Recreational Maths
I posted this in another forum, but thought some of you might be interested:

The Nearly Perfect Anti-Magic Square

Fill all of {1..9} into a 3x3 square so that all 19 numbers from {1..19} appear either as a cell value or a sum/product of a row/column/diagonal.

The answer is unique (not counting reflections/rotations). :idea:

Something to occupy the time waiting for Richard's results on the 6-rod problem. :ugeek:
Author:  Para [ Sat May 24, 2008 12:43 am ]
Post subject:  Re: Recreational Maths
udosuk wrote:
Fill all of {1..9} into a 3x3 square so that all 19 numbers from {1..19} appear either as a cell value or a sum/product of a row/column/diagonal.


That was kinda fun. Not too difficult.

Answer

Hidden Text:
856
419
372
Author:  udosuk [ Sat May 24, 2008 4:50 am ]
Post subject:  Re: Recreational Maths
Well done Para! ;clapclap;

When you say "not too difficult" did you acquire help from a computer? If you found it manually then it's truly a great effort! More so if you also proved the uniqueness! :salute:
Author:  Para [ Sat May 24, 2008 5:33 pm ]
Post subject:  Re: Recreational Maths
Hi

Yeah i did it manually. Dunno about proving uniqueness. :whistle: Just set a few basic things first.
Hidden Text:
There is a max of 10 different sums/products between 10-19 possible, which means we need 2 doubles: both product and sum. The 2 doubles(136=10/18 and 128=11/16 which is the only possibility) and how they thus had to cross and the fact that somewhere twice 1 of {67} and {89] had to be in a row/column/diagonal somehere together and this had to equal to 19 once{379/469/478/568} and the other one is 15/17{267/269/467}.

Worked with that. And kinda assumed what the center cell had to be.

Para
Author:  udosuk [ Sun May 25, 2008 5:26 am ]
Post subject:  Re: Recreational Maths
Excellent work Para, but the fact that you have to guess the centre cell dents the elegancy a little bit. :geek:
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