Griddlers Strategy Guide
Griddlers (aka Nonograms) begin with an empty grid with numbers on top (or bottom) and on one side. Your goal is to 'chisel' out a picture in the grid using the numbers as clues. Each number tells you how big a string of filled in squares are needed. Example, having "3,2" as a clue means you are going to need to find 3 consecutive, filled in squares, then at least one square not filled in, then 2 consecutive, filled in squares. Squares not filled in are usually marked with a dot or a small 'x'. Figuring out which squares need to be filled in, and thereby discovering a picture, is what makes Griddlers fun.
Before I get into the strategies themselves, let me show you a counting technique I use. When you are added numbers, add an additional one except for the last number. This reflects the need for a space between each string of filled in squares. For example, "2,3,3" should be added in your head as "3+4+3 = 10". Some may find it easy to simply add a number by one automatically than thinking "2+1+3+1+3". If this confuse you, it will be illustrated in my second strategy.
I order the bits of strategies from simple to most complex. For fill in squares, I use '#'. For squares you know won't be filled in, I use 'x'. For squares where the result is still not known, I use '_'.
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ONE: Perfect fit / Empty
This is obvious. If the clue is one number equal to the size of the grid, then fill it all in! Likewise, a clue of 0 means nothing is filled in. X it all out. So on a 10x10...
# # # # # # # # # # 10
x x x x x x x x x x 0
TWO: Perfect fit in parts
Using the counting technique, if it adds up to the grid size, you likewise can fill and x out all squares according to the clue numbers. Using the "2,3,3" in a 10x10 example again, it will look like this.
# # x # # # x # # # 2,3,3
THREE: Overlap fit
If the clue is a single number that is greater than half the size of the grid, you know that you can fill some of the middle squares together. In a 10x10, that will be anything larger than a 6. To illustrate this, assume we have a row with a clue '6' and we fill it out on the left and right.
# # # # # # _ _ _ _ 6
_ _ _ _ # # # # # # 6
As you can see, the middle two are filled in for both cases. So you can safely fill in those squares:
_ _ _ _ # # _ _ _ _ 6
FOUR: Can't fit
If you x out some squares, and the string of unknown squares are smaller than the clue, you can x those out too. For example, consider this.
_ _ _ _ _ _ x _ _ x 5
There is no way that string of 5 can fit between those two x squares. So x them out:
_ _ _ _ _ _ x x x x 5
FIVE: Partial line overlap
Lets combine the last two strategies by continuing using or last example. If you count out 5 from the left and 5 from the right (just left of the left most x), you know that four squares have to be filled in. So:
_ # # # # _ x x x x 5
Again, you can do this when the clue is greater than half of the string of unknown squares. 5 is greater than half of 6 (3), in this case.
SIX: Multiple overlaps
The above clues will be enough to get you through all easy griddlers. Eventually though you need to do this strategy. Hard griddlers will demand this out of you A LOT.
To begin, you need to count off from one side what you know (strategy 3), but with multiple numbers with the counting technique. Start with the largest number clue. Count off to one side till you reach the last square for the large number in question. Note that. Do the same for the other side. If you don't pass that square you noted, you can't use this strategy. If you do, start filling in that noted square plus all the others you can fill while counting.
Lets use "2,4,1" in a 10x10 grid. If you mentally count off 3+4, or 7 from the left....
# # _ # # # # _ _ _ 2,4,1
... and 2+4 from the right (remember! One plus one for the x plus four!)...
_ _ _ _ # # # # _ # 2,4,1
... you will see 3 squares can be filled in.
_ _ _ _ # # # _ _ _ 2,4,1
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As you can see, you may need to combine strategies to find squares you can fill in or rule out. Sometimes this just fall into place. Take these examples.
_ _ _ _ _ # _ _ _ _ 2,1
Here you can't do diddly.
_ _ _ _ _ # # _ _ _ 2,1
Now we can do something. We found our string of '2', so place an x on each side of it and, since nothing is to the left of it, x all of squares to the left too.
x x x x x # # x _ _ 2,1
That leaves only 2 unknown squares, one of which is filled in. One more.
_ _ # _ _ _ # _ _ _ 2,1
You can tell that those 3 unknown squares in the middle can't all be filled in; the right filled in square have to be the '1' and the one on the left have to be part of the '2'. Since we got our '1', lets x out the square to the left and right of it, along with all of the squares on the right.
_ _ # _ _ x # x x x 2,1
As for the '2', either the square to the immediate left or the immediate right is filled in, but we don't know which. All the others we can rule out. So it know looks like this.
x _ # _ x x # x x x 2,1
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I like to show you two more things before concluding. Note these are far more complex examples. They expand on the sixth strategy.
1) If you have a large number on the end (instead of the middle), use the counting technique and see how far it goes. If it is close enough to the end, you know you can fill in some squares. Take this 15x15 example.
_ _ _ _ _ | _ _ _ _ _ | _ _ _ _ _ 7,4
That may not look possible at first glance. But if you count 5+7, you get 12. Since griddlers are often portioned into mini-grids of 5x5, it will be easy to spot what that twelfth square will be.
<= count 5+7=12
_ _ _ # _ | _ _ _ _ _ | _ _ _ _ _ 7,4
That is within the 7 squares from the left! So you know every square to the left of it, within those 7 left most squares, are filled in.
_ _ _ _ # | # # _ _ _ | _ _ _ _ _ 7,4
Now let do the same from the left to the right. 8+4 is 12 (again), so the twelfth square is...
count 8+4=12 =>
_ _ _ _ # | # # _ _ _ | _ # _ _ _ 7,4
... which is just barely the fourth square. All other you don't know anything about.
2) For those you don't mind number-crunching instead of counting, here is another thing you can do to improve the sixth strategy. Lets use a 20x20 illustration!
_ _ _ _ _ | _ _ _ _ _ | _ _ _ _ _ | _ _ _ _ _ 7,2,1,4
You CAN count it out like I just shown you. But if your want harder proof than clumsy counting, do this. First, take the grid size, add one, subtract the number of clue numbers, then the number of filled in squares. (Yep, our counting technique is buried in that equation). In our example, the grid size is 20, the number of clue numbers is 4, and the number of filled in squares is 7+2+1+4 or 14.
Grid Size + 1 - Number of Clue Numbers - Number of Filled In Squares
20 + 1 - 4 - 14 = 3.
That number tells you that any clue number greater than that number has something of it that can be filled in. To find out how much, take the clue number and subtract this number you just found; ignore the negative values.
7,2,1,4
7-3,2-3,1-3,4-3
4,-1,-2,1
4,_,_,1
So we can fill in four of the '7' and one of the '4'. Now we got this. Count it out if you like as I shown you and you will see.
_ _ _ # # | # # _ _ _ | _ _ _ _ _ | _ # _ _ _ 7,2,1,4
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Late in a griddler you might go around in circles. With a row clue you finish a row, but that square makes you finish a column, which finish another row, which finish another column, etc. around and around. Or you may mark enough squares off to form areas, and with the clue numbers you got, you know where each consecutive string of squares are in a row or column, but still can't fill any of it in! Remember! NEVER ASSUME ANYTHING! If you have to, fiddle around on a scratch paper on what may be and then make your rulings on what you now know as is. Also look for counterexamples. Say you think these squares should be filled in, but not sure. Can you think of another example? If so, forget it and try something else.
And finally, if you are well beyond stuck and about to go iNsAnE, don't! Here is an online solver you can use.
Have fun!
posted by Patricio @ 1:04 PM
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