Puzzle Corner

prpr said:
You can fill in Column B, then the middle of row 3.
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Yes, and then I get stuck. Same thing happens on most examples of this puzzle. I  can find the solution, but not using logic. Unless you count trial and error as logic - I don't. By that I mean filling in values and then backtracking/rubbing out when it fails. Now if I did it in my head rather than on the grid, is that logical Spock?
 
EEPhil said:
Unless you count trial and error as logic - I don't.
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No I don't.
EEPhil said:
Now if I did it in my head rather than on the grid, is that logical Spock?
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Could be. I do it that way if possible, but sometimes you can't keep all the detail in your head without writing it down.
Rule out the impossible, write down the possible, then eliminate the impossible step by step by rows and columns either by inspection or by eliminating pairs or triples.
B2, B3, B4, B1, C3, D3, D2, E5, C4, C5, D5, A5, A4, A3, A1, E4, D4, E3, E2, E1, D1, C1, C2
 
prpr said:
Rule out the impossible, write down the possible, then eliminate the impossible step by step by rows and columns either by inspection or by eliminating pairs or triples
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That is my method. Usually, quite early, I get to the point where I can't see futher moves. Then I resort to what I've called trial and error. Sometimes that reveals I've missed an obvious, logical, move. More likely it's a case of "if this, then that" until I end up with (for example) two 4s on the same line. I have to write it down, my short term memory often fails because I'm easily distracted. (That's my excuse and I'm sticking to it). I'm not very good at chess either.
 
Here's how I solved Sunday's (in full gory detail):–

First the "gimmes". In Column B: "5" can't be less than anything, so for column B has to be at B4; "2" and "1" follow from the "3" in A2; and that just leaves B1 for "3". "1" can't be greater than anything so for Row 2 has to be at D2:

1658735907354.png

Next, I mark possible numbers in each box which has constraints. Constraints can be limitations due to chains of inequality signs, or due to numbers already in that row or column. For brevity, I use the position of dots to represent numbers as follows:

1658735743002.png

1658736753589.png

A3 and E3 can only be "4" or "5", which eliminates the possibility of "4" and "5" appearing anywhere else in Row 3, so D3 can only be "3" and consequently C3 has to be "2". In Column E, "3" can be nowhere other than E5, and that forces C4 and C5:

1658737067347.png

...which allows Row 5 to be completed:

1658737281054.png

...which then allows Row 4 to be completed, and the rest just falls into place:

1658737472399.png
 
Managed both, on second attempt. In both cases got stuck after obvious moves. Decided to start again from scratch and managed to complete them without guessing. Spotting two squares that can only be (eg) 2 or 5 in one line, and that this means the other three squares cannot contain those numbers, seems to be the key to my difficulties. I often miss them!
 
EEPhil said:
Spotting two squares that can only be (eg) 2 or 5 in one line, and that this means the other three squares cannot contain those numbers, seems to be the key to my difficulties. I often miss them!
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That's the key, yes, and sometimes there is a chain of those to fathom.
 
I wonder what your first two moves are! Yes, maybe it's harder than I thought when I did it yesterday:
E3=1
[A3 B3 C3]=[3 4 5] ∴︎ D3=2
[A1 C1 E1]=[1 2 3] ∴︎ [B1 D1]=[4 5]
[B1 B3]=[4 5] ∴︎ [B2 B5]=[1 2] ∴︎ B4=3
!!! [D1 D4]=[4 5] ∴︎ [D2 D5]=[1 3], [A2 B2 D2]=[1 2 3] ∴︎ E2=5 E3=4...
 
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1 and 2 in row 3. Then stuck without trial and error. (Found the result)
Not sure about your A1,C1,E1 assertion. A1 can only be 1 or 2, surely.
Hang on, B3 can't be 3! -> A3=[2,1],A2=1,A1=0! B4 not B3?
 
Pending? After the bottom row and one other 5 I was stuck again.
Might have another go from scratch later.
 
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