July 2019 - Page 2

axn · 2019-07-02, 02:28

Quote:

Originally Posted by a1call

But at least you didn't have to use your programming skills this time.

Ah, but you see, I did have to use it

a1call · 2019-07-02, 03:03

Good, my data mining worked.

Thanks.
I will still try it the old fashioned way for now. Getting too old for programming.

LaurV · 2019-07-02, 07:29

This is not really a puzzle, it is more like a prank.

That huge "size 40" tricked me a little, until I realized that for 14 moves to be a cycle you can move maximum 7 steps in one direction, as you will need 7 steps to come back. Therefore, jumping two squares every time, there is no way to reach the other end of a "size 40" board (the standard chess board is "size 8", not "size 64", grrr). Then it clicked to me they mean area, or the number of squares, and in this case you can't have a board too large. A 6x7 board will be already larger, so you must stay in 5x8, or 6x6, or you still can play with a 10x4. The Nx3 would be too narrow, I mean, the only way you can make a non-intersecting track with length 14 is on a 14x3 board, and that is already "size 42", isn't it??? And then "bang!" it hit me! haha.

It took me like 10 minutes.

Edit: pencil and paper, no code, no calculator for area. (Long Live Mathologer, one of his videos shows how to calculate area of tilted rhombuses, by wrapping them in imaginary non-tilted square boxes and subtract the surrounding area).

axn · 2019-07-02, 08:03

Quote:

Originally Posted by LaurV

Long Live Mathlogger

Mathologer?

LaurV · 2019-07-02, 08:35

Quote:

Originally Posted by axn

Mathologer?

Grr.. fixed, and sorry for this stupid typing mistake - one of the things I hate most is making fun of people's names...

Dieter · 2019-07-05, 13:06

Am I right with the following summing up:

Each vertex is belonging to two edges (and not more!).

It is forbidden that 3 consecutive points lie in a straight line, because :

„Two edges meeting at a corner are usually required to form an angle that is not straight (180°); otherwise, the collinear line segments will be considered parts of a single side.“
(Wiki, simple polygon)

uau · 2019-07-05, 18:38

I don't believe the intent was to forbid two consecutive jumps in the same direction.

You could interpret it as saying that the geometric shape surrounded by the path must be a simple polygon. Said simple polygon might have fewer vertices than there are jumps in the path, if consecutive jumps are in the same direction.

Dieter · 2019-07-12, 15:11

Quote:

Originally Posted by uau

I don't believe the intent was to forbid two consecutive jumps in the same direction.

You could interpret it as saying that the geometric shape surrounded by the path must be a simple polygon. Said simple polygon might have fewer vertices than there are jumps in the path, if consecutive jumps are in the same direction.

Probably you are right. Fortunately it doesn‘t matter - there is at least one solution without these problems.

yae9911 · 2019-07-21, 12:06

Nothing was said about the side lengths of the path polygon, so any number of consecutive moves in the same direction is allowed.
"board of size mXn" was chosen instead of "board of area ...." to avoid interference with the enclosed area of the knight's path.

Kebbaj · 2019-07-25, 00:04

for those who have found the solution.
and who is bored like me. try to find instead of a difference in area 7.
the product of both areas 195.

Dieter · 2019-07-25, 09:57

Quote:

Originally Posted by Kebbaj

for those who have found the solution.
and who is bored like me. try to find instead of a difference in area 7.
the product of both areas 195.

195=3*5*13, so the only realistic possibility is 13*15

It‘s no problem to find shapes with area 13 respectively 15.
Or I have misunderstood your problem...

2019-07-02, 07:29	#14
LaurV Romulan Interpreter Jun 2011 Thailand 9611₁₀ Posts	This is not really a puzzle, it is more like a prank. That huge "size 40" tricked me a little, until I realized that for 14 moves to be a cycle you can move maximum 7 steps in one direction, as you will need 7 steps to come back. Therefore, jumping two squares every time, there is no way to reach the other end of a "size 40" board (the standard chess board is "size 8", not "size 64", grrr). Then it clicked to me they mean area, or the number of squares, and in this case you can't have a board too large. A 6x7 board will be already larger, so you must stay in 5x8, or 6x6, or you still can play with a 10x4. The Nx3 would be too narrow, I mean, the only way you can make a non-intersecting track with length 14 is on a 14x3 board, and that is already "size 42", isn't it??? And then "bang!" it hit me! haha. It took me like 10 minutes. Edit: pencil and paper, no code, no calculator for area. (Long Live Mathologer, one of his videos shows how to calculate area of tilted rhombuses, by wrapping them in imaginary non-tilted square boxes and subtract the surrounding area). Last fiddled with by LaurV on 2019-07-02 at 08:33

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2019-07-02, 03:03	#13
a1call "Rashid Naimi" Oct 2015 Remote to Here/There 807₁₆ Posts	Good, my data mining worked. Thanks. I will still try it the old fashioned way for now. Getting too old for programming.

2019-07-05, 13:06	#17
Dieter Oct 2017 5·23 Posts	Am I right with the following summing up: Each vertex is belonging to two edges (and not more!). It is forbidden that 3 consecutive points lie in a straight line, because : „Two edges meeting at a corner are usually required to form an angle that is not straight (180°); otherwise, the collinear line segments will be considered parts of a single side.“ (Wiki, simple polygon)

2019-07-05, 18:38	#18
uau Jan 2017 3²·11 Posts	I don't believe the intent was to forbid two consecutive jumps in the same direction. You could interpret it as saying that the geometric shape surrounded by the path must be a simple polygon. Said simple polygon might have fewer vertices than there are jumps in the path, if consecutive jumps are in the same direction.

2019-07-21, 12:06	#20
yae9911 "Hugo" Jul 2019 Germany 31 Posts	Nothing was said about the side lengths of the path polygon, so any number of consecutive moves in the same direction is allowed. "board of size mXn" was chosen instead of "board of area ...." to avoid interference with the enclosed area of the knight's path.

2019-07-25, 00:04	#21
Kebbaj "Kebbaj Reda" May 2018 Casablanca, Morocco 89 Posts	for those who have found the solution. and who is bored like me. try to find instead of a difference in area 7. the product of both areas 195.