@How many squares on a go board.
Ray Tomes
"How many squares are there on a Go Board?"
There were four or five different answers, all predictable,
and all wrong. I suppose this was too big a clue really,
but how about it, how many do you think?
I will post the correct answer in a few days if no-one gets it.
Ray Tomes rto...@kcbbs.gen.nz
Lance A. Brown
properly designed gobans are rectangular in shape with a rectagular
grid on them. Therefore zero squares.
Lance
Jim Gillogly
Ray Tomes <Ray_...@kcbbs.gen.nz> wrote:
>"How many squares are there on a Go Board?"
>
>There were four or five different answers, all predictable,
I'm not too proud to supply a wrong answer... in fact I'll give two of 'em.
Answer 1: none. They're all rectangles, and on an official-sized board
they're not individually off square by enough to make 17x18 a square.
18
Answer 2: 2109 = sum i^2 on a cheap board with evenly-ruled lines.
i=1
That's 1 18x18 square, 4 17x17, 9 16x16, ..., 18^2 1x1.
--
Jim Gillogly
Highday, 10 Foreyule S.R. 1994, 21:38
Eric Swanson
Trivial: zero, since go boards are not square. But I suppose
you are looking for 2109.
A hippie geek
Well, on my good goban, there are 0 squares, but 324 rectangles.
I do have a cheap one that has 324 squares, but uses smaller plastic stones.
:)
--
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Steve MacGregor
I don't have my calculator with me, so I'll give my answer this way:
it's SIGMA(i=1,18) i^2.
--
Stefano MAC:GREGOR ==----= Steve MacGregor
(li) \ma-GREG-r\ ([.] [.]) Phoenix, AZ
----- Fenikso, Arizono, Usono ----------oOOo--(_)--oOOo----------------------
Dave Ring
Hmm. I think the ratio is 15/14. If that's true then there are 12 squares.
--
Dave Ring
dwr...@tam2000.tamu.edu
Jan van Loenen
:Ray Tomes <Ray_...@kcbbs.gen.nz> wrote:
:>Some years ago I asked the New Zealand Go Congress the question-
:>
:>"How many squares are there on a Go Board?"
:>
:>There were four or five different answers, all predictable,
:>and all wrong. I suppose this was too big a clue really,
:>but how about it, how many do you think?
:>I will post the correct answer in a few days if no-one gets it.
:>
:>Ray Tomes rto...@kcbbs.gen.nz
: Trivial: zero, since go boards are not square. But I suppose
: you are looking for 2109.
I think the answer is 1.
Horizontal lines are 2.4 cm apart, vertical lines 2.25 cm. So a block
of 15 x 16 lines makes a square with sides 36.
Jan
-----------
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brian r. mcdonald
2.25 cm) are correct, then the answer should be 20 squares, since
that many 15 line by 16 line squares can be defined on a 19 x 19
baord.
chiwito
--
part-time longshoreman and full-time dilettente at the game of go
bibliophile, skeptic, oulipian, liberal, romantic
"if you've got 'em by the balls, their hearts and minds will follow"
AC Missias
Ray_...@kcbbs.gen.nz (Ray Tomes) writes:
> "How many squares are there on a Go Board?"
How about 324? 19 x 19 board means only 18 x 18 squares (unless you
are being picky about rectangularity), since the 19 includes the
borders....
-ACM
/\ /\
/ o o \
\ \ / /
¡
David Carlton
> Some years ago I asked the New Zealand Go Congress the question-
> "How many squares are there on a Go Board?"
Infinitely many. You aren't specifying anything in particular about
where the corners or sides are, after all.
david carlton
car...@math.mit.edu
My nose feels like a bad Ronald Reagan movie...
Wilfred...@cs.cmu.edu
> The board is marked with nineteen vertical lines spaced 2.21 cm apart
and nineteen horizontal lines spaced 2.36 cm apart.
The ratio is 221/236 or .93644...
ti...@folabm.unisurg.akh-wien.ac.at
>What a brillant answer to an innocent question!
>
>fritz
>
OOps! I shot my own knee! I bow and hope you take my apologies!
Since my local netserver has had troubles, I did not get the original question, and thus,
not knowing that there is a puzzle online, I thought you were answering in a very unpolite
manner! Hope we will stay go friends?
fritz
Peter Lasersohn
>"How many squares are there on a Go Board?"
An infinite number. Of course they are not all marked by lines...
ti...@folabm.unisurg.akh-wien.ac.at
>:In article <16394333.3...@kcbbs.gen.nz>,
>:Ray Tomes <Ray_...@kcbbs.gen.nz> wrote:
>:>Some years ago I asked the New Zealand Go Congress the question-
>:>
>:>"How many squares are there on a Go Board?"
>:>There were four or five different answers, all predictable,
I looked up the measurements of an _official_ go board, and Jan van Loenen is right:
>Horizontal lines are 2.4 cm apart, vertical lines 2.25 cm. So a block
>of 15 x 16 lines makes a square with sides 36.
But there are 12 different 15x16 squares on a go board. (You need 16 of the nineteen
lines to make the 15-side and 17 of the other nineteen to create the 16 side - so there
are three parallel lines left on one side and four on the other. So you can move your 15x16 block
to twelve different positions.)
So I vote for 12 squares.
fritz
Dave Ring
>Hmm. I think the ratio is 15/14. If that's true then there are 12 squares.
Oops. 20 of course.
--
Dave Ring
dwr...@tam2000.tamu.edu
John Tromp
Well, a square can have length between 1 and 19 on a side, and the number
of possible placements on the grid equals the square of 19 minus this
length, so the answer is 1^2 + 2^2 + ... + 18^2 = 18 * 19 * 37 / 6 = 2109.
Unless you want to count 0x0 squares, in which case you add 361:-)
regards,
%!PS % -John Tromp (tr...@math.uwaterloo.ca)
42 42 scale 7 9 translate .07 setlinewidth .5 setgray/c{arc clip fill
setgray}def 1 0 0 42 1 0 c 0 1 1{0 3 3 90 270 arc 0 0 6 0 -3 3 90 270
arcn 270 90 c -2 2 4{-6 moveto 0 12 rlineto}for -5 2 5{-3 exch moveto
9 0 rlineto}for stroke 0 0 3 1 1 0 c 180 rotate initclip}for showpage
Ming Yuean Choy
: In article <16394333.3...@kcbbs.gen.nz>
: Ray_...@kcbbs.gen.nz (Ray Tomes) writes:
: -ACM
It's not as simple as that... You are only counting the smallest
squares. There are other size squares as well. Such as the bigger
squares made up of 4 small squares, and ones made up of 9 small squres,
etc. and the possibilities of over-lapping.
(Of course I'm also ignoring the pickiness of rectangularity. I think
the poster of this question did not intend that.)
Just a caution to those undertaking the task of calculating. But this is
enough for me :-) Not gonna dwell on anymore.
Ming,
ti...@folabm.unisurg.akh-wien.ac.at
>In article <16394333.3...@kcbbs.gen.nz>
>Ray_...@kcbbs.gen.nz (Ray Tomes) writes:
>
>> "How many squares are there on a Go Board?"
>
>How about 324? 19 x 19 board means only 18 x 18 squares (unless you
>are being picky about rectangularity), since the 19 includes the
>borders....
You are right!
As I explained yesterday, for a 15x16 block you have 12 different matches on a go-board.
Maybe I have a blind spot, and this solution is not the correct one, but we are NOT picky!
Go-boards ARE rectangular!! This is because far east culture is fond of assymmetry.
(And a good set of go-stones consists of white stones which are slightly smaller than the
black ones. This is because the shiny white ones _appear_ to be bigger than they really are!
This is, for such a simple thing, subtle, true art and most aesthetical!
greetings
fritz
John Tromp
> if the dimensions used to reach the answer of one square (2.4 cm x
rectangle you mean:-)
> 2.25 cm) are correct, then the answer should be 20 squares, since
> that many 15 line by 16 line squares can be defined on a 19 x 19
> baord.
Sorry, but you only get (19-15) * (19-16) = 4 * 3 = 12 of those.
For another 'standard' rectangle size of 22x24mm, the answer would
be (19-11) * (19-12) = 56.
brian r. mcdonald
: In article <chiwitoD...@netcom.com>, chi...@netcom.com (brian r. mcdonald) writes:
: > if the dimensions used to reach the answer of one square (2.4 cm x
: ^^^^^^
: rectangle you mean:-)
contain a square made up of 15 x 16 rectangles of the size given. i
merely pointed out that there are actually 20 such squares.
: > 2.25 cm) are correct, then the answer should be 20 squares, since
: > baord.
: Sorry, but you only get (19-15) * (19-16) = 4 * 3 = 12 of those.
: For another 'standard' rectangle size of 22x24mm, the answer would
: be (19-11) * (19-12) = 56.
20, as stated previously. a 15x16 square located in the upper left
corner would have as its right side the 15th vertical line. it could
then be moved 1, 2, 3, or 4 lines to the right, for 5 possible
positions. similarly, the bottom of the square could be on line 16,
17, 18, or 19. 5 x 4 = 20.
for the same reason, your other answer (for 22x24 mm lines) is 72.
C
C
C
then be moved 1, 2, 3, or 4 lines to the right, making five possible
: regards,
: %!PS % -John Tromp (tr...@math.uwaterloo.ca)
: 42 42 scale 7 9 translate .07 setlinewidth .5 setgray/c{arc clip fill
: setgray}def 1 0 0 42 1 0 c 0 1 1{0 3 3 90 270 arc 0 0 6 0 -3 3 90 270
: arcn 270 90 c -2 2 4{-6 moveto 0 12 rlineto}for -5 2 5{-3 exch moveto
: 9 0 rlineto}for stroke 0 0 3 1 1 0 c 180 rotate initclip}for showpage
Ray Tomes
--------------------------
A few days ago I asked the question:
warning, the silliest ones weren't as silly as when I did it
live some years ago. The answers received on either occasion
from least clever upwards are ...
361 This rates zero thinking. It is the number of vertices.
324 This has one quantum of thought. It recognises that the
number of lines is 19, but spaces are 18. 324=18x18
2109 This has an insight. There are larger squares that are
2x2 and 3x3 etc all the way up to 18x18 of the smaller
squares. 2109 = 1x1 + 2x2 + ... + 18x18
0 This has a bit of speciallist knowledge. The ancient
chinese (I think) decided that to overcome perspective
they would make them rectangles. It also makes the stones
sit in an interesting way, as the stone sizes are between
the two different directions grid sizes.
20 Just because they are rectangles, doesn't mean that you
can't make a square out of them. The standard Nihon Ki-in
board size is 42.42 by 45.45 cm which is exactly in the
ratio 14:15. Therefore if you look for a 14 high by 15
wide block of rectangles, you will get a square!
On this basis there are (19-15)x(19-14) = 4x5 = 20
30 or 56 You are on the right track. It does depend on the board.
42 Actually the above logic does depend on the exact board
measurements, which do vary. It also depends on the little
empty space around the edge of the board being in the same
proportions, which it is not. When the verge which is of
equal width on all sides (don't ask me why) is taken off,
the remaining part is found to be very close the proportions
12:13. I like this proportion, because it means that there
are (19-12)x(19-13) = 7 x 6 = 42 squares on a go board.
So there you are Douglas Adams fans, the ultimate question about
life the universe and everything is:
How many squares are there on a Go Board?
All those who answered zero and now want to claim that the little
rectangles wont make squares because the ratio isn't exactly in
the proportion 12:13 can give up now. Unless you actually
considered the arguements beyond the zero answer above, you
don't get full marks.
Ray Tomes rto...@kcbbs.gen.nz
Fred R. Stearns
brian r. mcdonald <chi...@netcom.com> wrote:
>John Tromp (tr...@math.uwaterloo.ca) wrote:
>: In article <chiwitoD...@netcom.com>, chi...@netcom.com (brian r. mcdonald) writes:
>: > if the dimensions used to reach the answer of one square (2.4 cm x
>: ^^^^^^
>: rectangle you mean:-)
>no, i meant "one square"; a previous poster claimed that a goban would
>contain a square made up of 15 x 16 rectangles of the size given. i
>merely pointed out that there are actually 20 such squares.
>: > 2.25 cm) are correct, then the answer should be 20 squares, since
>: > that many 15 line by 16 line squares can be defined on a 19 x 19
>: > baord.
>
>: Sorry, but you only get (19-15) * (19-16) = 4 * 3 = 12 of those.
>: For another 'standard' rectangle size of 22x24mm, the answer would
>: be (19-11) * (19-12) = 56.
>20, as stated previously. a 15x16 square located in the upper left
>corner would have as its right side the 15th vertical line. it could
>then be moved 1, 2, 3, or 4 lines to the right, for 5 possible
>positions. similarly, the bottom of the square could be on line 16,
>17, 18, or 19. 5 x 4 = 20.
I must come to the defense of my friend John Tromp. The goban as
you know is 19x19 lines, which form 18x18 (little) rectangles.
The 15x16 must be 16 goban rectangles wide (as the rectangles are
narrower than they are tall) and 15 high. The right rectangle of
the 15x16 would be in the 16th rectangle of the goban, and the
bottom rectangle of the 15x16 would be in the 15th rectangle. So
you can move it right 2 more spaces so that the 16th rectangle of
the 15x16 corresponds with either the 16th, 17th, or 18th
rectangle of the goban. You can move it down 3 more spaces so
that the bottom rectangle of the 15x16 corresponds with one of
the 15th, 16th, 17th, or 18th rectangles. This gives you 3 * 4 =
12.
But, as the original poster of this question points out, the
ratio of the width versus the height of the goban varies, so
there is more than one answer along those lines.
I wonder if the ideal ratio might not be an irrational number in
which case the number of squares you could build out of the
little rectangles would be zero.
brian r. mcdonald
1999yi...@gmail.com
public static void main(String[] args) {
int tmp1 = 0, tmp2 = 0, sum = 0;
for (int i = 1; i <= 18; i++) {
// X-axis j from 1 to I
// Y axis Z from 1 to I
// calculate of two transient values of x-axis y-axis
for (int j = 1; j < i; j++) {
tmp1 = 18 / j;
for (int z = 1; z < i; z++) {
tmp2 = 18 / z;
sum += tmp1 * tmp2;
}
}
}
System.out.println("sum:" + sum);
}
---------------------------------------
And the answer is 36535
Rainer Rosenthal
> ---------------------------------------
> And the answer is 36535
>
Hint: look closely at your board!
In case you bought it in a normal shop you won't find one single square.
But in case you made it yourself or it was home-made by a friend then
there might be many of them.
Well, I was wrong ... This is what sensei's library has for this
question: 42. (Famous answer :-) )
https://senseis.xmp.net/?HowManySquaresOnAGoBoard
Cheers,
Rainer
Thomas Rohde
> […]
Rainer Rosenthal
:-)