### Brain Teasers

# Diagonal Possibility

Fill the eight spaces below with numbers from 1 to 8. No number that comes before or after any other number should be placed in an adjacent space, either horizontally, vertically or diagonally.

(For Example 2 should not be next to the number 1 or the number 3)

The arrangement of the space is

* __ __ *

__ __ __ __

* __ __ *

(For Example 2 should not be next to the number 1 or the number 3)

The arrangement of the space is

* __ __ *

__ __ __ __

* __ __ *

### Answer

* 3 5 *7 1 8 2

* 4 6 *

Other possibilities are mirror images of the above answer.

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## Comments

Unless I'm mistaken, you could have worded the question better. You seem to have left out the horizontal limitation, so one could have a number of other solutions e.g. 1,2 in top row 5,6,7,8 in middle row and 3,4 in bottom row ... and a bunch of combinations of these where there are no consecutive numbers vertically/diagonally next to each other.

Well, he's right, but I assumed the horizontal limitation and go the correct answer.

That was a great one!!! I actually got the answer!!

You seem to have left out the horizontal but a good one

i was lost from the start

cool

The horizontal must have been changed in the edit so no worries there. I got it EASY until I found out that my setup was wrong due to the way it looks in the puzzle (hexagon with one additional space to the right). When I started to look at the answer I saw the setup was different, quickly hid it, and went to solve it again. This time it was fun figuring it out!

Great teaser, though I would recommend some way to get the spaces lined up properly:

^^__ __ ^^

__ __ __ __

^^__ __ ^^

Carats seem to work great!

Great teaser, though I would recommend some way to get the spaces lined up properly:

^^__ __ ^^

__ __ __ __

^^__ __ ^^

Carats seem to work great!

I see the dilemma here... the carat idea worked great when I initially typed it! Oh, well!

i found another solution

*1 5*

3 8 2 7

*6 4*

*1 5*

3 8 2 7

*6 4*

No that is not possible as 1 is diognal to 2.

Testing, testing- does this transfer from windowed input to fixed form with less distortion? (The O's would be replaced with digits; the X's would be considered nul or blanks.

XOOX

OOOO

XOOX

XOOX

OOOO

XOOX

Another test - 0's not O's.

X00X

0000

X00X

X00X

0000

X00X

Nov 11, 2006

Good one. This probably teaches good strategies of distribution.

Jan 31, 2007

Here is another solution:

13

5796

24

13

5796

24

That's not it....You have placed 9 instead of 8. If 8 comes it would be beside 7...

After seeing the difficulty score, I thought this one would take a while, but people must have been overthinking it. It took me three tries over the course of about 3 minutes to get the correct lineup. Fun.

3 minutes? Try 15 seconds. It's immediately obvious that either 1 or 8 has to go in the middle of the hexagon, leaving only one place for the adjacent number. Repeat that for the other central location with the other digit with a single neighbor and the puzzle essentially fills itself out.

How does this make the top three list of "fun" problems or get the difficulty rating it has?

How does this make the top three list of "fun" problems or get the difficulty rating it has?

The top row must be either 35 or 53 or 46 or 64

The middle row must be 7182 or 2817

The bottom row must be either 35 or 53 or 46 or 64 (of course it cannot use the same 2 numbers as the top row and the order of the middle row sets the order of the top and bottom rows to keep the 3 from being diagonal to the 2 or the 6 from being diagonal to the 7)

So there are 2 * 2 * 1 = 4 combinations:

53 & 2817 & 64

35 & 7182 & 46

46 & 7182 & 35

64 & 2817 & 53

These 4 combinations are the only possible solutions

The middle row must be 7182 or 2817

The bottom row must be either 35 or 53 or 46 or 64 (of course it cannot use the same 2 numbers as the top row and the order of the middle row sets the order of the top and bottom rows to keep the 3 from being diagonal to the 2 or the 6 from being diagonal to the 7)

So there are 2 * 2 * 1 = 4 combinations:

53 & 2817 & 64

35 & 7182 & 46

46 & 7182 & 35

64 & 2817 & 53

These 4 combinations are the only possible solutions

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