## Heightmazes

Notes on possible new logic puzzles

### Re: Heightmazes

ixsetf wrote:Maybe I am confused about the rules, but for squares like r1c5 wouldn't there be multiple valid answers? Neither a 1 or a 2 would produce an immediate contradiction, and since it is not connected to the rest of the grid its value has no effect on the height values on the rest of the puzzle. I am unclear how you would go about making a determination about which value is correct.

Depends on what's in r2c5. If, for example, r2c5 is a 3, then in r1c5, 1 would be legal, and 2 would not.

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

### Re: Heightmazes

Smythe Dakota wrote:Depends on what's in r2c5. If, for example, r2c5 is a 3, then in r1c5, 1 would be legal, and 2 would not.

Bill Smythe

I was under the impression that the "wall" between them meant that the value of r2c5 wasn't a factor? Am I incorrect in that assumption?
ixsetf

Posts: 50
Joined: 11 May 2014

ixsetf wrote:r1c5---is not connected to the rest of the grid,
its value has no effect on the height values on the rest of the puzzle

it is connected

numbers in r12c5
must justify the given wall between those cells

Pat

Posts: 3882
Joined: 18 July 2005

### Re:

Pat wrote:
ixsetf wrote:r1c5---is not connected to the rest of the grid,
its value has no effect on the height values on the rest of the puzzle

it is connected

numbers in r12c5
must justify the given wall between those cells

Ah, I knew there must have been something I was missing, I just couldn't figure out what.

That definitely limits the possibility for multiple solutions, and increases the amount of logic involved quite a bit.
ixsetf

Posts: 50
Joined: 11 May 2014

### Re: Heightmazes

evert wrote:Another 10x10 puzzle:

This seems a good puzzle,but with your image (i'm not good at quoting images)

- start box top left is 7,7 and Bottom-right is 14 (space) 13, 10

i can see MULTIPLE answers for this puzzle.

the top line - (example) can be

2, 1, 1, 4, 2, 2, 1

2, 2, 1, 4, 2, 2, 2

2, 2, 1, 4, 2, 2, 3

2, 2, 1, 4, 2, 3, 2

2, 2, 1, 4, 2, 3, 3

2, 2, 1, 4, 2, 3, 4 etc..... all these numbers can appear in the top-right line of your solution, & be valid answers....
gordonisnz

Posts: 8
Joined: 11 November 2016

### Re: Heightmazes

gordonisnz wrote:i can see MULTIPLE answers for this puzzle.

the top line - (example) can be

2, 1, 1, 4, 2, 2, 1
2, 2, 1, 4, 2, 2, 2
2, 2, 1, 4, 2, 2, 3
2, 2, 1, 4, 2, 3, 2
2, 2, 1, 4, 2, 3, 3
2, 2, 1, 4, 2, 3, 4 etc..... all these numbers can appear in the top-right line of your solution, & be valid answers....

The (whole) top line can only be

7, 7, 6, 2, 1, 1, 4, 2, 4, 5

Note that the last cell cannot be 2, 3, or 4, because it must differ from the cell below by at least 2. Similarly, between cell 8 and cell 9, there must be a difference of at least 2.

Regards,

Mike Metcalf

m_b_metcalf
2017 Supporter

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Location: Berlin

### Re: Heightmazes

m_b_metcalf wrote:
gordonisnz wrote:The (whole) top line can only be

7, 7, 6, 2, 1, 1, 4, 2, 4, 5

Note that the last cell cannot be 2, 3, or 4, because it must differ from the cell below by at least 2. Similarly, between cell 8 and cell 9, there must be a difference of at least 2.

Regards,

Mike Metcalf

i must re-read the instructions. from what i understood, any adjacent cell/box must be the same value or +/- 1 - I didnt pick up on a "difference of 2",or see that in any of the examples/pictures provided.
gordonisnz

Posts: 8
Joined: 11 November 2016

### Re: Heightmazes

gordonisnz wrote:i must re-read the instructions. from what i understood, any adjacent cell/box must be the same value or +/- 1 - I didnt pick up on a "difference of 2",or see that in any of the examples/pictures provided.

If there's a wall between two cells then it cannot be jumped over and so the difference between them cannot be 0 or 1.

Regards,

Mike Metcalf

m_b_metcalf
2017 Supporter

Posts: 11455
Joined: 15 May 2006
Location: Berlin

### Re: Heightmazes

m_b_metcalf wrote:
gordonisnz wrote:i must re-read the instructions. from what i understood, any adjacent cell/box must be the same value or +/- 1 - I didnt pick up on a "difference of 2",or see that in any of the examples/pictures provided.

If there's a wall between two cells then it cannot be jumped over and so the difference between them cannot be 0 or 1.

what about cells with NO wall between them ?
gordonisnz

Posts: 8
Joined: 11 November 2016

### Re: Heightmazes

gordonisnz wrote:what about cells with NO wall between them ?

" must be the same value or +/- 1"

m_b_metcalf
2017 Supporter

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Joined: 15 May 2006
Location: Berlin

### Re: Heightmazes

m_b_metcalf wrote:
gordonisnz wrote:what about cells with NO wall between them ?

" must be the same value or +/- 1"

So - the top-right corner has 3, 3,3 - the blank squares above them can have multiple values that are correct... - no single solution..

gordonisnz

Posts: 8
Joined: 11 November 2016

### Re: Heightmazes

gordonisnz wrote:So - the top-right corner has 3, 3,3 - the blank squares above them can have multiple values that are correct... - no single solution..

The eighth cell in the top row is constrained by the cell below to be 2, 3, or 4. Of these three values, only 2 fulfils the constraint arising from the 4 in cell seven.

HTH

Mike Metcalf

m_b_metcalf
2017 Supporter

Posts: 11455
Joined: 15 May 2006
Location: Berlin

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