## AIC Problem

Post the puzzle or solving technique that's causing you trouble and someone will help

### AIC Problem

Below is a puzzle in which I thought I had found an AIC.

1[r2c1]=1[r6c2]-1[r5c2]=9[r5c2]-9[r3c2]=9[r1c2]

I would have thought that r2c1 cannot be 9 and r1c2 cannot be 1.

This is not the case…… r2c1 is 9 while r1c2 can have the 1 excluded.

Where lies the error? Thanks for your help.

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`   *--------------------------------------------------------------------* | 8      1269   7      | 129    3      1269   | 2569   4      59     | | 19     4      16     | 129    5      7      | 2369   236    8      | | 5      269    3      | 4      8      269    | 1      267    79     | |----------------------+----------------------+----------------------| | 6      8      25     | 137    17     4      | 235    9      135    | | 3      19     4      | 159    2      1589   | 7      18     6      | | 19     7      25     | 6      19     38     | 2345   238    345    | |----------------------+----------------------+----------------------| | 7      136    9      | 25     4      25     | 8      136    13     | | 2      136    16     | 8      179    139    | 3469   5      13479  | | 4      5      8      | 1379   6      139    | 39     137    2      | *--------------------------------------------------------------------*`
Jasper32

Posts: 60
Joined: 04 January 2008

### Re: AIC Problem

Jasper32 wrote:Below is a puzzle in which I thought I had found an AIC.

1[r2c1]=1[r6c2]-1[r5c2]=9[r5c2]-9[r3c2]=9[r1c2]

I would have thought that r2c1 cannot be 9 and r1c2 cannot be 1.

This is not the case…… r2c1 is 9 while r1c2 can have the 1 excluded.

Where lies the error? Thanks for your help.

Hi Jasper32,

I guess =1[r6c2] should be =1[r6c1]?

Your error lies in the last strong link: 9[r3c2]=9[r1c2] is not a strong link, there is a third 9 in both column 2 (r5c2) and block 1 (r2c1).
hobiwan
2012 Supporter

Posts: 321
Joined: 16 January 2008
Location: Klagenfurt

It did seem like a lot of 9's in box 1 and column 2 but it looked like it might be OK but, of course, it wasn't.

I guess I had a convoluted view which went something like this:

I assumed when 9[r5c2] was a strong link that either of the other two 9's, r1c2 or r3c2, in column 2 could
be made a weak link. That to me meant the the remaining 9 would be a strong link. I will not try that trick
again and I want to thank you for pointing out the error of my ways. I did it something like once before and it was
sucessful which must have been just plain dumb luck on my part.

Thanks again,

Jasper32
Jasper32

Posts: 60
Joined: 04 January 2008

Jasper32 wrote:I assumed when 9[r5c2] was a strong link that either of the other two 9's, r1c2 or r3c2, in column 2 could
be made a weak link. That to me meant the the remaining 9 would be a strong link.

=9[r5c2] causes both 9s (r1c2 and r3c2) to be false. One alone is incorrect. Your original AIC would have meant, that r5c2 and r1c2 are 9, which is of course impossible since they are in the same row.

But: Because r1c2 and r3c2 are in the same box, they form a group link which forces r2c1 to be 9. So you could write:

1[r2c1]=1[r6c2]-1[r5c2]=9[r5c2]-9[r13c2]=9[r2c1]

This is a continuous loop, but it doesnt eliminate anything.
hobiwan
2012 Supporter

Posts: 321
Joined: 16 January 2008
Location: Klagenfurt