Brainy 2

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March 17th 2009, 01:38 AM
u2_wa

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Brainy 2

Fit digits 1 to 8 in such a way that no two consecutive numbers are next to each other.
An example is also attached.
Please count your attempts!
March 17th 2009, 07:18 AM
Soroban

Hello, u2_wa!

This is an excellent puzzle!

Quote:

Place the digits 1 to 8 so that no two consecutive numbers are adjacent.
("Adjacent" numbers are in cells that share a side or a vertex.)

Code:

*---* | | *---*---*---* | | | | *---*---*---* | | | | *---*---*---* | | *---*

I solved this while in college (back in the Jurassic Period)
. . and have a logical solution.

I'll post it later, after everyone has tried it.
March 17th 2009, 07:57 AM
masters

Quote:

Originally Posted by u2_wa

Fit digits 1 to 8 in such a way that no two consecutive numbers are next to each other.
An example is also attached.
Please count your attempts!

Hi u2_wa,

I have no logical approach to this one, but through trial and many errors, I came up with this. I'll 'white' it out, in case others are still struggling and want to solve it.

Code:

| 2 | -------------- | 6 | 8 | 5 | -------------- | 4 | 1 | 3 | -------------- | 7 |
March 17th 2009, 09:37 AM
ADARSH

Quote:

Originally Posted by masters

Hi u2_wa,

I have no logical approach to this one, but through trial and many errors, I came up with this. I'll 'white' it out, in case others are still struggling and want to solve it.

Code:

| 2 | -------------- | 6 | 8 | 5 | -------------- | 4 | 1 | 3 | -------------- | 7 |

Believe it or not I got that solution on 2nd or 3rd try but unfortunately I was searching for the number of solutions to this problem before I read your posts (Giggle)

Quote:

Please count your attempts!

Uncountable steps after solving the problem :D in 3rd
March 17th 2009, 11:22 PM
u2_wa

Quote:

Originally Posted by ADARSH

Believe it or not I got that solution on 2nd or 3rd try but unfortunately I was searching for the number of solutions to this problem before I read your posts (Giggle)

Uncountable steps after solving the problem :D in 3rd

Hello ADARSH:
I also did it in the second attempt, let us see what others do!!
March 18th 2009, 01:27 PM
Soroban

Okay, here's my "logical" approach to this puzzle.

We have the eight cells labeled $a$ to $h$ .
There are two "central cells", $c$ and $h.$

Code:

*---* | a | *---*---*---* | b | c | d | *---*---*---* | e | f | g | *---*---*---* | h | *---*

There are eight digits to install:
. . two "end" numbers and six "middle" numbers.

. . $\underbrace{1}_{\text{end}},\underbrace{2,3,4,5,6, 7}_{\text{midde}},\underbrace{8}_{\text{end}}$

Place a middle number in a central cell, say, 4 in cell $c$ .

Code:

*---* | x | *---*---*---* | x | 4 | x | *---*---*---* | x | x | x | *---*---*---* | h | *---*

We see that its neighbors (3 and 5) cannot be placed
. . in cells $a,b,d,e,f,g.$
So both 3 and 5 cannot be installed.

Conclusion: the central cells must not contain a middle number.

Hence, 1 and 8 must go in cells $c$ and $f.$

Code:

*---* | a | *---*---*---* | b | 1 | d | *---*---*---* | e | 8 | g | *---*---*---* | h | *---*

2 cannot be in cells $a,b,d,e,g \quad\Rightarrow\quad 2 \in h.$

7 cannot be in cells $b,d,e,g \quad\Rightarrow\quad 7 \in a.$

Code:

*---* | 7 | *---*---*---* | b | 1 | d | *---*---*---* | e | 8 | g | *---*---*---* | 2 | *---*

3 cannot be in $e$ or $g$ . . . 3 may be in $b$ or $d.$

Pick one: say, $3 \in b$

Code:

*---* | 7 | *---*---*---* | 3 | 1 | d | *---*---*---* | e | 8 | g | *---*---*---* | 2 | *---*

6 cannot be in $d.$

Also, 6 cannot be in cell $e.$
Else 4 and 5 will be in cells $d$ and $g$ (and be adjacent).
. . Hence: . $6 \in g.$

Code:

*---* | 7 | *---*---*---* | 3 | 1 | d | *---*---*---* | e | 8 | 6 | *---*---*---* | 2 | *---*

4 cannot be in cell $e$ . . . $4 \in d$

And finally: . $5 \in e$

Code:

*---* | 7 | *---*---*---* | 3 | 1 | 4 | *---*---*---* | 5 | 8 | 6 | *---*---*---* | 2 | *---* Solution

Disregarding rotations and reflections, there is one solution.