Rather than hi-jack the creativity thread, here is a puzzle from New Scientist that needs a type of creativity to solve it.

Draw 7 straight lines through a chess board so that there is at least one line passing through each square.

With convoluted creative thinking I managed to convince myself that it was a trick question and that it can’t be done.

That is the wrong answer.

I was really annoyed with myself when I saw the right one.

The Rev Dodgson said:

Rather than hi-jack the creativity thread, here is a puzzle from New Scientist that needs a type of creativity to solve it.

Draw 7 straight lines through a chess board so that there is at least one line passing through each square.

With convoluted creative thinking I managed to convince myself that it was a trick question and that it can’t be done.

That is the wrong answer.

I was really annoyed with myself when I saw the right one.

Is that the one where some of the lines extend beyond the borders of the board?

Tamb said:

The Rev Dodgson said:

Rather than hi-jack the creativity thread, here is a puzzle from New Scientist that needs a type of creativity to solve it.

Draw 7 straight lines through a chess board so that there is at least one line passing through each square.

With convoluted creative thinking I managed to convince myself that it was a trick question and that it can’t be done.

That is the wrong answer.

I was really annoyed with myself when I saw the right one.

Is that the one where some of the lines extend beyond the borders of the board?

No, that was a related one which I got right (but cheated by having seen it before).

The Rev Dodgson said:

Tamb said:

The Rev Dodgson said:

Rather than hi-jack the creativity thread, here is a puzzle from New Scientist that needs a type of creativity to solve it.

Draw 7 straight lines through a chess board so that there is at least one line passing through each square.

With convoluted creative thinking I managed to convince myself that it was a trick question and that it can’t be done.

That is the wrong answer.

I was really annoyed with myself when I saw the right one.

Is that the one where some of the lines extend beyond the borders of the board?

No, that was a related one which I got right (but cheated by having seen it before).

Thanks.

My idea:

Diagonal lines that don’t run through the apexes, but instead start along the side (say halfway). That way the line crosses both black and white diagonal lines.

Michael V said:

My idea:

Diagonal lines that don’t run through the apexes, but instead start along the side (say halfway). That way the line crosses both black and white diagonal lines.

Yes, that gets you part way, but if you make an invalid assumption about the arrangement of the lines, you are always left with one square left over.

The Rev Dodgson said:

Rather than hi-jack the creativity thread, here is a puzzle from New Scientist that needs a type of creativity to solve it.

Draw 7 straight lines through a chess board so that there is at least one line passing through each square.

With convoluted creative thinking I managed to convince myself that it was a trick question and that it can’t be done.

That is the wrong answer.

I was really annoyed with myself when I saw the right one.

Hmm, I can see how to cover 63 squares. By setting each line slightly off horizontal, each of the 7 lines can cover 9 squares – eight in a row plus one more. 7*9 = 63.

mollwollfumble said:

The Rev Dodgson said:

Rather than hi-jack the creativity thread, here is a puzzle from New Scientist that needs a type of creativity to solve it.

Draw 7 straight lines through a chess board so that there is at least one line passing through each square.

With convoluted creative thinking I managed to convince myself that it was a trick question and that it can’t be done.

That is the wrong answer.

I was really annoyed with myself when I saw the right one.

Hmm, I can see how to cover 63 squares. By setting each line slightly off horizontal, each of the 7 lines can cover 9 squares – eight in a row plus one more. 7*9 = 63.

I think the maximum squares that one line can cover is 15, but there are four fundamentally different ways of drawing a line to cover 15 squares.

Is that on the right track?

On 7Mate Megastructures is doing that sea launch system.

mollwollfumble said:

The Rev Dodgson said:

Rather than hi-jack the creativity thread, here is a puzzle from New Scientist that needs a type of creativity to solve it.

Draw 7 straight lines through a chess board so that there is at least one line passing through each square.

With convoluted creative thinking I managed to convince myself that it was a trick question and that it can’t be done.

That is the wrong answer.

I was really annoyed with myself when I saw the right one.

Hmm, I can see how to cover 63 squares. By setting each line slightly off horizontal, each of the 7 lines can cover 9 squares – eight in a row plus one more. 7*9 = 63.

Mmmm, I’m finding it easy to get 63 by various ways!
I’ll keep trying.

dv said:

mollwollfumble said:

The Rev Dodgson said:

Rather than hi-jack the creativity thread, here is a puzzle from New Scientist that needs a type of creativity to solve it.

Draw 7 straight lines through a chess board so that there is at least one line passing through each square.

With convoluted creative thinking I managed to convince myself that it was a trick question and that it can’t be done.

That is the wrong answer.

I was really annoyed with myself when I saw the right one.

Hmm, I can see how to cover 63 squares. By setting each line slightly off horizontal, each of the 7 lines can cover 9 squares – eight in a row plus one more. 7*9 = 63.

Mmmm, I’m finding it easy to get 63 by various ways!
I’ll keep trying.

I suspect the answer involves two sets of intersecting oblique (but not diagonal) lines

mollwollfumble said:

The Rev Dodgson said:

Rather than hi-jack the creativity thread, here is a puzzle from New Scientist that needs a type of creativity to solve it.

Draw 7 straight lines through a chess board so that there is at least one line passing through each square.

With convoluted creative thinking I managed to convince myself that it was a trick question and that it can’t be done.

That is the wrong answer.

I was really annoyed with myself when I saw the right one.

Hmm, I can see how to cover 63 squares. By setting each line slightly off horizontal, each of the 7 lines can cover 9 squares – eight in a row plus one more. 7*9 = 63.

Yeah, that’s where I got to, and actually used pseudo-logical arguments to convince myself that that is the best that can be achieved.

mollwollfumble said:

mollwollfumble said:

The Rev Dodgson said:

Rather than hi-jack the creativity thread, here is a puzzle from New Scientist that needs a type of creativity to solve it.

Draw 7 straight lines through a chess board so that there is at least one line passing through each square.

With convoluted creative thinking I managed to convince myself that it was a trick question and that it can’t be done.

That is the wrong answer.

I was really annoyed with myself when I saw the right one.

Hmm, I can see how to cover 63 squares. By setting each line slightly off horizontal, each of the 7 lines can cover 9 squares – eight in a row plus one more. 7*9 = 63.

I think the maximum squares that one line can cover is 15, but there are four fundamentally different ways of drawing a line to cover 15 squares.

Is that on the right track?

No.

Hmm, just when you think you’ve done it, there’s one left over.

Bubblecar said:

Hmm, just when you think you’ve done it, there’s one left over.

So, so true.

The Rev Dodgson said:

mollwollfumble said:

mollwollfumble said:

Hmm, I can see how to cover 63 squares. By setting each line slightly off horizontal, each of the 7 lines can cover 9 squares – eight in a row plus one more. 7*9 = 63.

I think the maximum squares that one line can cover is 15, but there are four fundamentally different ways of drawing a line to cover 15 squares.

Is that on the right track?

No.

Well I’ve given up so let us know eventooally

Would it be cheating to just code this up and do a brute force search…

dv said:

Would it be cheating to just code this up and do a brute force search…

I think that would be cheating, although it would also be an interesting exercise.

I’ll post a link to an Excel file with the solution, and you can enter the number of lines you want to see.

The Rev Dodgson said:

dv said:

Would it be cheating to just code this up and do a brute force search…

I think that would be cheating, although it would also be an interesting exercise.

I’ll post a link to an Excel file with the solution, and you can enter the number of lines you want to see.

Yeah … I don’t think I’m going to get it.

Link for the solution.

https://1drv.ms/x/s!Aq0NeYoemF0niKcWzdhbgif13rAkXg

It should open with no lines displaying, but if someone else is looking and has displayed all the lines, I guess you’ll see that too.

The Rev Dodgson said:

Link for the solution.

https://1drv.ms/x/s!Aq0NeYoemF0niKcWzdhbgif13rAkXg

It should open with no lines displaying, but if someone else is looking and has displayed all the lines, I guess you’ll see that too.

Fair enough. I daresay I would have solved it if I hadn’t lost interest quite quickly :)

The Rev Dodgson said:

Link for the solution.

https://1drv.ms/x/s!Aq0NeYoemF0niKcWzdhbgif13rAkXg

It should open with no lines displaying, but if someone else is looking and has displayed all the lines, I guess you’ll see that too.

Huh.

I was actually kind of on the right track.

I just added an extra line and found the solution to be quite trivial.

sibeen said:

I just added an extra line and found the solution to be quite trivial.

rofl

The Rev Dodgson said:

Link for the solution.

https://1drv.ms/x/s!Aq0NeYoemF0niKcWzdhbgif13rAkXg

It should open with no lines displaying, but if someone else is looking and has displayed all the lines, I guess you’ll see that too.

That just opens hotmail for me.

my son got it in three goes… smart arse..

Arts said:

my son got it in three goes… smart arse..

kids – ay?

The Rev Dodgson said:

Arts said:

my son got it in three goes… smart arse..

kids – ay?

don’t worry I adequately scolded him…

Arts said:

The Rev Dodgson said:

Arts said:

my son got it in three goes… smart arse..

kids – ay?

don’t worry I adequately scolded him…

But seriously, it’s obvious once you see it, but if you are focussed on imagining all the lines sloping the same way it’s easy not to see it.

So congrats to smart-arse son.

Michael V said:

The Rev Dodgson said:

Link for the solution.

https://1drv.ms/x/s!Aq0NeYoemF0niKcWzdhbgif13rAkXg

It should open with no lines displaying, but if someone else is looking and has displayed all the lines, I guess you’ll see that too.

That just opens hotmail for me.

That’s odd.

It should open on-line Excel.

The Rev Dodgson said:

Link for the solution.

https://1drv.ms/x/s!Aq0NeYoemF0niKcWzdhbgif13rAkXg

It should open with no lines displaying, but if someone else is looking and has displayed all the lines, I guess you’ll see that too.

Oh, clever, two at each end.

And the other lines 7, 11, 12, 12, 11, 7 = 60.

Not at all obvious. Nice symmetry.

If you want another problem that seems impossible but isn’t, my favourite is “cut an equilateral triangle into four pieces that can be reassembled to make a square”. The answer is all over the web, but try it without looking up the answer.