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=========
A Hexagons Widget
Web: http://www.tux.org/~bagleyd/puzzles.html
Download: Primary site: ftp://ftp.tux.org/pub/tux/bagleyd/xpuzzles
Secondary site: ftp://ibiblio.org/pub/Linux/games/strategy
Maintainer: David A. Bagley <bagleyd@tux.org>
Try resizing the puzzle. Notice the puzzle resizes to take advantage of
the "room" available.
Try editing the file Hexagons.ad to get a certain feature and then copying
to $(HOME)/Hexagons (where Hexagons is the file name) and running
xhexagons again. There is also a Windows port (whexagons).
If you were looking for a auto-solver, sorry.
Refer to the man page for detailed command line options and instructions
on how to operate.
If you want further information on puzzles, I'll be glad :-) to send
it to you.
MATHEMATICAL STUFF USED IN CONSTRUCTION
Lets start out with a triangle of hexagons for simplicity's sake
and then expand these ideas to a hexagon of hexagons
Assuming it is a triangle of i hexagons in each row and the
numbering starts from 1.
Corner 1-> 1
2-> i(i+1)/2 - i + 1
3-> i(i+1)/2
Center ->i%3 =>
1: (2i'-1)*(2i')/2-i'+1 where i'= (i+2)/3
default: None
Max_Width -> i * 3^(1/2) units
Max_Height -> (3/2)i+(1/2) units
Start -> x= i * 3^(1/2)/2 units
y=0
fin=i
step=i
Next -> (n==fin) =>
true: x+= -3^(1/2) * (2 * step - 1)/2 units; y+=3/2 units;
step++; fin+=step
default: x+= 3^(1/2) units
Same row? -> (m'==n') where s'=(1+sqrt_trunc(1+8*(s - 1)))/2 {k}
i.e. s = s'(s'-1)/2
Same trbl? -> (m-1)-m'(m'-1)/2 == (n-1)-n'(n'-1)/2 {i}
Same tlbr? -> (m'+1)m'/2-m == (n'+1)n'/2-n {j}
Now assuming it is a hexagon of i hexagons in each row and
the numbering starts from 1.
Corner 1-> 1
2-> i
3-> Center - i + 1
4-> Center + i - 1
5-> 3i(i-1) - i + 2
6-> 3i(i-1) + 1
Center -> 3i(i-1)/2 + 1
Max_Width -> (2i-1) * 3^(1/2) units
Max_Height -> 3i-1 units
Start -> x= i * 3^(1/2)/2 units
y=0
fin=i
step=i
Next -> (n<=center) =>
true: (n==fin)
true: x+= -3^(1/2) * (2 * step - 1)/2 units; y+=3/2 units;
step++; fin+=step
default: x+= 3^(1/2) units
default: (n==fin)
true: step--; x+= -3^(1/2) * (2 * step - 1)/2 units;
y+=3/2 units; fin+=step
default: x+= 3^(1/2) units
Same row? -> (m'==n') {k} where (s<=center) =>
true: s' = (1+sqrt_trunc(1+8*(s+i*(i-1)/2)))/2-i
i.e. s = s'*(2s'-1)-(i)(i-1)/2
default: s' = 3*i-2-(1+sqrt_trunc(1+8*(3i(i-1)+1+i*(i-1)/2-s)))/2)
Same trbl? -> (m''==n'') {i} where (s<=center) =>
true: s'' = (s+i*(i-1)/2)-(s'+i)*(s'+i-1)/2
default: s'' = 2*i-2-(3i(i-1)+i*(i-1)/2-s-(3*i-s'-2)*(3*i-s'-3)/2)
Same tlbr? -> (m''==n'') {j} where (s<=center) =>
true: s'' = -1-((s+i*(i-1)/2)-(s'+i+1)*(s'+i)/2)
default: s'' = 2*i-1+(3i(i-1)+i*(i-1)/2-s-(3*i-s'-1)*(3*i-s'-2)/2)
FOUND A BUG?
Send bugs reports and fixes to the author. For bugs, please include
as much information as to their location as possible, since I may not
be able to duplicate them.
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