## Solve without guessing or making an assumption?

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

### Solve without guessing or making an assumption?

Code: Select all
`8 ? 6 | 4 9 5 | ? ? 1? 3 ? | 8 7 6 | 5 9 ?5 9 ? | ? ? ? | 8 6 ?=====================4 5 3 | 1 6 8 | 2 7 9? 6 9 | ? 4 ? | ? 5 87 ? 8 | 5 ? 9 | 4 ? 6=====================3 4 ? | 6 ? ? | 9 8 56 8 ? | 9 5 3 | ? 4 ?9 ? 5 | ? 8 4 | 6 ? 3`

I often get to this stage where there are no more obvious next steps (well, obvious to me). I can usually only finish them by making a guess/assumption and following through to success or failure.

Are there any tips/tricks to use at this stage?

sydneydenizen

Posts: 2
Joined: 19 June 2005

You need to guess in order to complete the grid...

This can mean two things:
a) it's not a Pappocom puzzle
b) you missed a clue
Animator

Posts: 469
Joined: 08 April 2005

a) it's not a Pappocom puzzle
You might be right. This puzzle is out of the Sydney Morning Herald and they don't seem to be listed on this website.

b) you missed a clue
I'm not sure what other clues there are that I would have missed? The numbers are exactly as I have posted them.
sydneydenizen

Posts: 2
Joined: 19 June 2005

Then you need to guess. There is no other way to complete it
Animator

Posts: 469
Joined: 08 April 2005

No guess is required.

Code: Select all
`  8   2-7   6  |  4    9    5  | 3-7  2-3   1 1-2   3    .  |  8    7    6  |  5    9   2-4  5    9    .  |  .    .    .  |  8    6   247  -------------+---------------+-------------  4    5    3  |  1    6    8  |  2    7    9 1-2   6    9  |  .    4    .  | 1-3   5    8  7   1-2   8  |  5    .    9  |  4   1-3   6  -------------+---------------+-------------  3    4    .  |  6    .    .  |  9    8    5  6    8    .  |  9    5    3  |  .    4    .  9    .    5  |  .    8    4  |  6    .    3`

Though Pappocom rates this as "arguably unfair", it can be solved by FCP (Forcing Chains Proof) in any number of places. For example:

Consider r5c7 and its relationship to r2c1:

1) r5c7 must be 1 or 3.
2) If r5c7=1 => r5c1=2 => r2c1=1
3) If r5c7=3 => r1c7=7 => r1c2=2 => r2c1=1

Since all possibilites for r5c7 lead to r2c1=1, then r2c1 MUST be 1. The rest of the puzzle solves quickly.

See http://forum.enjoysudoku.com/viewtopic.php?t=692
tso

Posts: 798
Joined: 22 June 2005

tso wrote:Consider r5c7 and its relationship to r2c1:

1) r5c7 must be 1 or 3.
2) If r5c7=1 => r5c1=2 => r2c1=1
3) If r5c7=3 => r1c7=7 => r1c2=2 => r2c1=1

Si
See http://forum.enjoysudoku.com/viewtopic.php?t=692

Nonsense!!!

r5c7=1 forces r6c2 to be 2
if r6c2 is 2 then r5c1 must be 1 and not 2
datprogrammer

Posts: 18
Joined: 22 June 2005

Nonsense!!!

r5c7=1 forces r6c2 to be 2
if r6c2 is 2 then r5c1 must be 1 and not 2

eh? TSO's reasoning looks fine to me!

r5c7=1 forces r6c2 to be 2

How so?
Last edited by simes on Sun Dec 11, 2011 2:33 pm, edited 1 time in total.
simes

Posts: 324
Joined: 11 March 2005
Location: UK

datprogrammer wrote:
tso wrote:Consider r5c7 and its relationship to r2c1:

1) r5c7 must be 1 or 3.
2) If r5c7=1 => r5c1=2 => r2c1=1
3) If r5c7=3 => r1c7=7 => r1c2=2 => r2c1=1

Si
See http://forum.enjoysudoku.com/viewtopic.php?t=692

Nonsense!!!

r5c7=1 forces r6c2 to be 2
if r6c2 is 2 then r5c1 must be 1 and not 2

You've made a mistake. As it turns out, in the completed puzzle, r5c7=1 and r5c1=2. Though it IS possible for something false to imply something true, it is NOT possible for something true to imply something false. Therefore there can be NO line of reasoning in which r5c7=1 (true) forces r5c1=1 (false).
tso

Posts: 798
Joined: 22 June 2005

### Humble Pie anyone

I'm hanging my head in shame - it seems I'm no longer able to understand cartesean co-ordinates.

I'll slink away slowly into the sunset and hope that one day I willbe forgiven for being so stupid!

My only possible defense is that I had just woken up and was yet to have my caffeine hit!

My apologies - I'm not usually so dense - honest!!!
datprogrammer

Posts: 18
Joined: 22 June 2005