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logical thinking
Jankonyex
Kwon-Tom Obsessive
Puzzles: 5680
Best Total: 9m 35s		Posted - 2006.12.10 18:51:19
counting + close loop
it's too long and too complicated to explain,
it include all properties of all numbers(include properties of assumptions.[e.g. If "2" and "3" are at position (x,y) and (x+1,y-1) respectively, assuming one cross at the top of "2" can get 3 lines, 2 crosses and more than 5 informations]), all rules and all assumption methods,
I've already explained a very little part in here, here, and also here.
I'll explain them some day.

I'm now sharing some very very common and basic patterns.






















going to bed...


Edit: Oh! I miss one very important thing to say.
May be I explain it by using one of the examples I've posted in topic 151:
I omit the "?"(s).
¡@¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä
¡U¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¡@¡@¡@£A¡@¡@¡@¡@¢Ø¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¡@¡@¡@¢ô¡@¢ü¡@¡@¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¢õ¢Ó¢ù¢Õ¢ý¡Ï¡@¡Ï¡U
¡U£A¡@¡@¡@¡@¡@¢ö¡@¢ú¡@¢þ¡@¡@¡U
¡U¡Ï£A¡Ï¡@¡Ï¡@¡Ï¢÷¢Ô¢û¢Ö£@¡Ï¡U
¡U¡@¡@£A¡@¢ð¡@¡@¡@¢ø¡@£A¡@¡@¡U
¡U¡Ï¢é¢Ï¢í¢Ñ¢ñ¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡U
¡U¡@¡@¢ê¡@¢î¡@¢ò¡@¡@¡@¡@¡@£A¡U
¡U¡Ï¡@¡Ï¢ë¢Ð¢ï¢Ò¢ó¡Ï¡@¡Ï¡@¡Ï¡U
¡U¡@¢×¡@¡@¢ì¡@£A¡@¡@¡@¡@¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡U
¡@¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã
there're only two points A and B to allow lines to go into region I
a+b = c+d = e = f+g = 1
there're only two points C and D to allow lines to go into region I
e+f = g = h+i = j+k = 1 (* i+j =\= 2)
there're only two points E and F to allow lines to go into region J
l+m+n = o+p = q = r+s = 1 (* n+o =\= 2)
there're only two points G and H to allow lines to go into region J
q+r = s = t+u = v+w = 1

get:
e = g = q = s = 1 , f = r = 0

one more example:
¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡@¡Ï
¡@¡@¡@¡@¡@¡@£A¡@¡@¡@¡@¢Ø¡@
¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡@¡Ï
¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@
¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¢Ð¡@¡Ï¡@¡Ï
£A¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@
¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï
¡@¡@£A¡@¡@¡@¡@¡@¡@¡@£A¡@¡@
¡Ï¡@¡Ï¡@¢Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï
¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@£A
¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡@¡Ï
¡@¢×¡@¡@¡@¡@£A¡@¡@¡@¡@¡@¡@
¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡@¡Ï

if region I and J both have even number of endpoint(s), A and B are both at corner{\}
if region I and J both have odd number of endpoint(s), features of A and B are similar to the previous example.

Edit:

¡Ï£A¡Ï¡@¡Ï£B¡Ï
£A¡@¡@¡@¡@¡@£B
¡Ï£A¡Ï¡@¡Ï£B¡Ï
£A¡@¡@¢²¡@¡@£B
¡Ï£A¡Ï¡@¡Ï£B¡Ï
¡@¡@£B¡@£B¡@£B
¡Ï¡@¡Ï£B¡Ï£B¡Ï

x and y are two crosses such that x connects y to form at most one anticlockwise circle by using other cross(es),
there're no other positive numbers except this "3" in that region and at least one positive number out that region,
deduced that there're mainly no lines other than that "3" in that region and at least one thing around that "3" can be deduced.
Last edited by Jankonyex - 2007.03.02 13:18:21
kiwigeek
Kwon-Tom Noob
Puzzles: 4		Posted - 2006.12.11 15:26:21
Uh, it's hard to tell on those examples where one little puzzle ends and the next begins.
procrastinator
Kwon-Tom Obsessive
Puzzles: 1083
Best Total: 12m 56s		Posted - 2006.12.12 01:36:39
Quote:
Originally Posted by jankonyex



You'll need to explain this. Certainly I can't infer what the ?s should be like in your other puzzles; they can all (by symmetry) be lines or crosses:



There are some combinations that can't exist, though: each pair must contain one line and one cross.
Last edited by procrastinator - 2006.12.12 01:38:13
jamin
Kwon-Tom Obsessive
Puzzles: 1233
Best Total: 27m 9s		Posted - 2006.12.12 12:19:09
Quote:
Originally Posted by jankonyex



I would have thought it would have been
chairman
Kwon-Tom Obsessive
Puzzles: 1397
Best Total: 17m 32s		Posted - 2006.12.12 12:52:27
I think it means that you must enter the 2332 block in the north west and leave it in the south east (or vice versa), which is more or less what procrastinator says. Similarly, there are only two ways to traverse a 1331 block, either east-west, or north-south.   

The question marks have the same value.
Gadget1903
Kwon-Tom Addict
Puzzles: 325
Best Total: 23m 39s		Posted - 2006.12.12 14:47:36
Quote:
Originally Posted by procrastinator
Quote:
Originally Posted by jankonyex



You'll need to explain this. Certainly I can't infer what the ?s should be like in your other puzzles; they can all (by symmetry) be lines or crosses:

Maybe that's the point each pair must be a line and a cross.  look what happens to other squares on the diagonal...i.e. look at the situation where a 1 or a 3 is on the 2's or 1's diagonal to the 2332 or 1331 pattern.





1331 requires both 1's to get the diagonal property...

but I think you only need one of the two 2's to get the diagonal property for 2332...or another way to look at it, the two 3's make the 2 into a 'parallel 2'

I think that if you analyze the 2332 pattern closely you will also see that it contains two simpler patterns...



Jankonyex
Kwon-Tom Obsessive
Puzzles: 5680
Best Total: 9m 35s		Posted - 2006.12.12 16:01:58
Quote:
Originally Posted by gadget1903

1331 requires both 1's to get the diagonal property...
you're right, and one "3" is already enough.
Quote:
Originally Posted by gadget1903

but I think you only need one of the two 2's to get the diagonal property for 2332...
I'm sorry, I don't understand.
Quote:
Originally Posted by gadget1903

I think that if you analyze the 2332 pattern closely you will also see that it contains two simpler patterns...
I better rewrite this pattern as:

Gadget1903
Kwon-Tom Addict
Puzzles: 325
Best Total: 23m 39s		Posted - 2006.12.12 18:54:21
Quote:
Originally Posted by jankonyex

Quote:
Originally Posted by gadget1903

but I think you only need one of the two 2's to get the diagonal property for 2332...
I'm sorry, I don't understand.
I mixed it up, you don't need the 2nd two for the 2332 pattern...but you do need it for the diagonal property, as your updated version makes clear.
Gadget1903
Kwon-Tom Addict
Puzzles: 325
Best Total: 23m 39s		Posted - 2006.12.12 23:51:59
Here is a common pattern I found...
Jankonyex
Kwon-Tom Obsessive
Puzzles: 5680
Best Total: 9m 35s		Posted - 2006.12.13 09:18:44
Quote:
Originally Posted by gadget1903
Here is a common pattern I found...
oh ya I miss this
Jankonyex
Kwon-Tom Obsessive
Puzzles: 5680
Best Total: 9m 35s		Posted - 2007.01.14 11:43:14
Sepicial case of counting in one square:
Hidden numbers:
If there's a nubmer A, that means there're A lines surround this number,
so if there're A lines surround a number X, X = A.

¡Ï¢é¡Ï
¢ê¢Ï¢ë
¡Ï¢ì¡Ï

e.g.
¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï
¡@¡@¡ý¡@¡@¡@¡@¡@£A¡@¡@¡@¡@
¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï
¡@¡@¡@¢±¡@¡@¡@¢±¡@¡@¡ý¡@¡@
¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï
¡@¡@¡@¡@¡@¢Ï¡@¡@¡@¢±¡@¡@¡@
¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï
¡@¡@¡@¡@¡@¡@¡@¢Ð¡@¡@¡@¡@¡@
¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï
¡@¡@¡@¡@¡@¢±¡@¡@¡@¢±¡@¡@¡@
¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï
¡@¡@¡@¡@¡ý¡@¡@¡@¡@¡@¡ý¡@¡@
¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï
is equivalent to
¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï
¡@¡@¡ý¡@¡@¡@¡@¡@£A¡@¡@¡@¡@
¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï
¡@¡@¡@¢±¡@¡@¡@¢±¡@¡@¡ý¡@¡@
¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï
¡@¡@¡@¡@¡@¢±¡@¡@¡@¢±¡@¡@¡@
¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï
¡@¡@¡@¡@¡@¡@¡@¢±¡@¡@¡@¡@¡@
¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï
¡@¡@¡@¡@¡@¢±¡@¡@¡@¢±¡@¡@¡@
¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï
¡@¡@¡@¡@¡ý¡@¡@¡@¡@¡@¡ý¡@¡@
¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï

a very useful corner "2" is created.

something not directly related to counting:
In some very hard puzzles, it's difficult to make conclusion(s) by only few assumptions, so finding hidden numbers is also a good method.
____________________________________________________________________________________
Sometimes we can't find the hidden number, but we can also conclude things by counting:
¡Ï¡@¡Ï¡@¡Ï
¡@¢Ï¡@¢æ¡@
¡Ï¡@£C¡@¡Ï
¡@¢ç¡@¢Ð¡@
¡Ï¡@¡Ï¡@¡Ï
If by A's view, that's z, it's also true for by B's view, that's z,
no conclusion made by X or Y's view.
e.g.
¢÷: 1 line to pass through, regard as odd amount of line to pass through.
¢í: 0 line to pass through, regard as even amount of line to pass through.
¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï
¡@¡@¡ý¡@¡@¡@¡@¡@£A¡@¡@¡@¡@
¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï
¡@¡@¡@¢±¡@¡@¡@¢±¡@¡@¡ý¡@¡@
¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï
¡@¡@¡@¡@¡@¢Ï¡@¡@¡@¢±¡@¡@¡@
¡Ï¡@¡Ï¡@¡Ï¡@£C¡@¢÷¡@¡Ï¡@¡Ï
¡@¡@¡@¡@¡@¡@¡@¢Ð¡@¡@¡@¡@¡@
¡Ï¡@¡Ï¡@¡Ï¡@¢÷¡@¢í¡@¡Ï¡@¡Ï
¡@¡@¡@¡@¡@¢±¡@¡@¡@¢±¡@¡@¡@
¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï
¡@¡@¡@¡@¡ý¡@¡@¡@¡@¡@£A¡@¡@
¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï
z = e affecting A
¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï
¡@¡@¡ý¡@¡@¡@¡@¡@£A¡@¡@¡@¡@
¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï
¡@¡@¡@¢±¡@¡@¡@¢±¡@¡@¡ý¡@¡@
¡Ï¡@¡Ï¡@¢÷¡@¢í¡@¡Ï¡@¡Ï£A¡Ï
¡@¡@¡@¡@¡@¢Ï¡@¡@¡@¢±¡@¡@¡@
¡Ï¡@¡Ï¡@£C¡@¢í¡@¡Ï¡@¡Ï¡@¡Ï
¡@¡@¡@¢æ¡@¡@¡@¡@¡@¡@¡@¡@¡@
¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï
¡@¡@¡@¡@¡@¢±¡@¡@¡@¢±¡@¡@¡@
¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï
¡@¡@¡@¡@¡ý¡@¡@¡@¡@¡@£A¡@¡@
¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï
z = o affecting X

Actually, this is simple counting.
chairman
Kwon-Tom Obsessive
Puzzles: 1397
Best Total: 17m 32s		Posted - 2007.01.14 18:56:52
I like the idea of hidden numbers, never came into my mind. However, the examples are unreadable for me. They appear to be encoded. Or do I miss something?
Jankonyex
Kwon-Tom Obsessive
Puzzles: 5680
Best Total: 9m 35s		Posted - 2007.03.30 19:39:41
finding one unknown by counting in region(s):
I've written [jsl11] to explain this:
¡@¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡U
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¡U¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡U
¡U£A¢°¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¢±¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¢±¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¢±¡@¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¡@¡@¢±¡@¡@¡@¡@¡@¡@¡ý¡@¡@¢±¡@¡@£A¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@£C¡@¢÷¡@¢÷¡@¡Ï¡@¡Ï£A¡Ï¡U
¡U¡@¡@¡@¡@¡@¡@¡@¢±¡@¡@¡@¡@¡@¡@¡@¡@¡@¢±¡@¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¢÷¡@¡Ï¡@¡Ï¡@¡Ï¡@¢í¡@¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¢í¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¡@¡@¡@¡@¢±¡@¡@¡@¡@¡@¡@¡@¡@£A¡@£A¡@¡ý¡U
¡U¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡@¢÷¡@¡Ï£A¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¡@¡@¡@£A¡@¡@¡@£A¡@£A¡@¡@¡@¡@¡@¡@¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@£A¡@¡@¡@¡@¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡U
¡@¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã
z = e

In counting, we're region searchers.
the above explanation is simplified, original one's here:
¡@¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡U
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¡U¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡U
¡U£A¢°¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¢±¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¢±¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¢±¡@¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¡@¡@¢±¡@¡@¡@¡@¡@¡@¡ý¡@¡@¢±¡@¡@£A¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@£C¡@¢÷¡@¢÷¡@¡Ï¡@¡Ï£A¡Ï¡U
¡U¡@¡@¡@¡@¡@¡@¡@¢±¡@¡@¡@¡@¡@¡@¡@¡@¡@¢±¡@¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¢÷¡@¡Ï¡@¡Ï¡@¡Ï¡@¢í¡@¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¢í¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¡@¡@¡@¡@¢±¡@¡@¡@¡@¡@¡@¡@¡@£A¡@£A¡@¡ý¡U
¡U¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¢÷¡U
¡U¡@¡@¡@¡@¡@¡@£A¡@¡@¡@£A¡@£A¡@¡@¡@¡@¡@¡@¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@£A¡@¡@¡@¡@¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡U
¡@¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã
z = e

much more easier after deducing 3 crosses:
¡@¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡ý¡U
¡U¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡U
¡U£A¢°¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¢±¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¢±¡@¡@¡@¡@¡@¡@¡@¡@£A¡@£A¡@¡@¢±¡@¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡@¢÷¡@¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¡@¡@¢±¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@£A¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@£C¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡U
¡U¡@¡@¡@¡@¡@¡@¡@¢±¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@£A¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¢÷¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¢í¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¡@¡@¡@¡@¢±¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¡@¡@¡@£A¡@¡@¡@£A¡@£A¡@¡@¡@¡@¡@¡@¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡U
¡U¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@£A¡@¡@¡@¡@¡@¡@¡U
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï£A¡Ï¡@¡Ï¡@¡Ï¡U
¡@¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã¡Ã
z = e

in the other hand:
¡@¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä¡Ä
¡U¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡@¡Ï¡U
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z = e

it works even without four crosses:
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z = e

different views, different deductions:
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z = z = o

talk about complex counting someday if I've time.
Last edited by Jankonyex - 2007.03.31 06:03:59
MTB
Kwon-Tom Addict
Puzzles: 363
Best Total: 34m 58s		Posted - 2007.04.27 20:51:06
Has this pattern been noted by anyone yet?



I can get two lines out of this, based on logic from my activity and parity rules.  The diagonal of twos can actually consist of any odd number of twos and it will still work.
Naivoj
Kwon-Tom Addict
Puzzles: 314
Best Total: 33m 50s		Posted - 2007.04.28 02:17:35
Note that this strut-2 pattern can be found in user puzzle #93 that MTB  created today and also in #59 created Tuesday April 24.
m2e
Kwon-Tom Obsessive
Puzzles: 607
Best Total: 16m 43s		Posted - 2007.04.28 02:45:04
Quote:
Originally Posted by mtb
Has this pattern been noted by anyone yet?
I use that one quite a bit, used it quite a bit actually in the user created puzzles filled with 2s
procrastinator
Kwon-Tom Obsessive
Puzzles: 1083
Best Total: 12m 56s		Posted - 2007.04.28 04:19:54
Quote:
Originally Posted by mtb
Has this pattern been noted by anyone yet?

It's been mentioned in the forums somewhere. Also variations with a 1 or a 3 at one end.
Jankonyex
Kwon-Tom Obsessive
Puzzles: 5680
Best Total: 9m 35s		Posted - 2007.04.28 07:29:25
Quote:
Originally Posted by mtb
H..............k.
Every time I wanted to talk about this type of pattern, but I don't know where to start with. So I decided to post some easy cases and just left them there for people to observe (the top of page 3).

Just observe then.

For"1"





For"2"







For"3"





there're four little blanks around a big blank,
four little blanks can be split into A and B (totally 14 possibilities).

For "1"
there're N x's in A or 4-N x's in B
For "3"
there're N lines in A or 4-N lines in B

So if you assume N ?'s in A and forcing M ?'s in B, that M ?'s must be true.

further more, you can make controls in different situations
e.g.
Since 2 connected lines also make 2 crosses


If it force "?" to be "x", this "x" must be true

If it force "?" to be "line", this "line" must be true

This is simple control.
For advanced control, you need to learn more patterns/cases, including how to force loop, close loop, impossible layers(very useful in extreme puzzles[usually with close loop] and extremely useful in symmetric puzzles which include symmetric solution(s) [e.g. only 2 // lines must be included in the axis]), wrong counting... etc.
For complex control? hehe! Try my puzzles and experiment it yourselves.

How to make maximum useful moves is the basic of control.
e.g.

Of course this is not enough for solving a puzzle faster, you need to consider also what you can further deduce by using the deduction deduced.

Take a bath and sleep......

Edit (2007.06.24 16:43:35):
control is useful in assumptions (including analysis[e.g. loop length limitation])
it's important, lets make great assumptions!

assume: x's/lines, number of lines/x's, pattern of lines/x's state, etc.

asm corner{\}2

4+2 x's

asm corner{\}2

4 {\}

asm a cross

3 x's, 2 lines, 1 state

Edit:
Similarly if there're n little blanks around a big blank,
n little blanks can be split into group A and B,

For "1"
there're N x's in A or n-N x's in B
For "n-1"
there're N lines in A or n-N lines in B

So if you assume N ?'s in A and forcing M ?'s in B, that M ?'s must be true.
Last edited by Jankonyex - 2007.12.14 10:40:24
chairman
Kwon-Tom Obsessive
Puzzles: 1397
Best Total: 17m 32s		Posted - 2007.04.29 20:08:38
Quote:
Originally Posted by gadget1903
Puzzle 95: Are there any patterns to start this puzzle off with?

The only pattern that is one my list is


You could call this a pattern as well:
procrastinator
Kwon-Tom Obsessive
Puzzles: 1083
Best Total: 12m 56s		Posted - 2007.04.30 02:58:00
Quote:
Originally Posted by chairman
Quote:
Originally Posted by gadget1903
Puzzle 95: Are there any patterns to start this puzzle off with?

You could call this a pattern as well:

Then this is no more of a stretch:

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