Of knight and mouse

[Demonic God]

This quest is a punishment for me being unable to keep my bid... due to Chew... booo

A Knight of the Bell, riding a mighty steed, chases a mouse through the Plains of Tranquility, reasons unknown. The mouse will run in a singular direction, one step at a time, while the horse chases, 4 steps each.

Though, as the mouse is tiny, and amidst tall grass, it couldn't be seen, yet can be trampled, should the horse jumps on top of it. The problem being, while it's direction known, it's location isn't.

The question is as follow: Is there a strategy, which would assure the knight, that should he run long enough, that'd be the end of the pesky mice?

==============================================

Math version

• The knight starts at 0 on a long, infinite line
• The mouse starts somewhere on the positive direction, and will continue running that way, 1 step at a time, after the knight's move
• The knight's horse can only gallop 4 steps at a time, forward or backward
• The knight must jump on top of the mouse to kill it, and he'll know when he succeed

Question: Can you guarantee that the mouse will be killed?

All correct solutions are rewarded with 10 SCs. Duration extended until 3 days after Anniversary. Happy Anniversary!

 

Edited April 27, 2020 by Demonic God

[Miq]

Lies,

 

This quest will run for 32 minutes from now.

[Demonic God]

*sweats profusely*

[Ledah]

I mean, the knight just has to follow the mouse? He knows the direction...?

[Steno]

I already solved it anyway. DG just doesn't want to admit it

 

[Demonic God]

indeed. He knows the direction, but his horse could accidentally just jump over, instead of trampling the mouse

The mouse however, is a simple creature. It simply runs straight, caring not about the knight.

Edited April 21, 2020 by Demonic God

[Jubaris]

When you say his direction is known, do you mean like we know he is on route 66 just not where exactly on the route, or that he's heading north-ish, from somewhere unknown whether that be Paris-London or Istanbul-Moscow where we only know he's going up? 

And is there a limit to thos grass field or is it infinite? 

 

[Demonic God]

put simply, think of a straight line to infinity.

[Demonic God]

*sigh* @Steno wins the hidden unannounced creative meme solution!
Please send me a PM to choose one of these as your reward:

• An encouragement to keep working on Darvin's quest
• A swift kick to the ass
• First letter of Chew the Ett password
• A kind reminder that this is still a discrete math problem
• A picture of a Silver coin

Congratulation!

*wonders if he'll live til the end of Anniversary*

Edited April 21, 2020 by Demonic God

[Miq]

I applaud the timely  manner of swift buttock treatment.

[Steno]

All in favor of sending DG to ToA so lashtal can get him, give me upvotes.

 

 

 

 

*PS. this is a joke*

[Tissy]

What is the action of the knight? 
forward, backward?

Edited April 22, 2020 by Tissy

[Aia del Mana]

6 hours ago, Tissy said:

What is the action of the knight? 
forward, backward?

I did think the usual move were two forward and one to either side, but mayhap this were the wrong realm.

[Ungod]

Let me end the debate with the following solution:

The Knight of the Bell - a symbol of strength in mind and body -  was not going to be outwitted by a mouse.  His adversary was nothing; yet a challenge could not be refused. Not wanting to lose precious time, he decided to end it in one swift move. He dismounted and unfolded his armor, revealing a secret weapon (!) -  which blinked repeatedly and then purred. 

''No need to run anywhere'', he sat down in the grass, lighting up a cigarette.

 

Edited April 22, 2020 by Ungod

[Demonic God]

Tissy was the first to successfully solve the challenge!
 

Edited April 22, 2020 by Demonic God

[Demonic God]

Well, given the limited amount of people who participated, I'd guess it's time to post the answer to this sidequest xD
 

First, we notice that if the knight ends turn k on the nth square, it will kill the mouse if the mouse started at square n - k. This shall be the number we care about. We denote these starting points (n-k) as kill squares

Upon the next move, the knight may move to square n + 4 or n - 4, and the corresponding kill square would be (n+4) - (k+1) = n+3, or (n-4) - (k+1) = n-5. Therefore the kill square moves forward by 3 or backward by 5.

Anyone interested about number theory, should know by now, that as 3 and 5 are co-prime squares, you shall be able to construct a strategy to cover every squares with these "kill squares". Hence an optimal solution is easily found.

The easiest way, would be to move forward twice and backward once, which is : 3 x 2 - 5 = 1. Repeat this pattern and you shall end up marking all squares as kill squares

The most optimal pattern is as follow: 0  3  6  1  4  7  2  5  8 (repeat). No kill squares are visited twice, and given any starting position of the mouse, eventually its original squares would be marked as dead (and thus, also the mouse).

[Aia del Mana]

I am quite unclear as to how the knight may gallop backward five steps at a time, as in the stated rules, the knight's horse appears only to be able to gallop four at a time.

[Demonic God]

1 hour ago, Aia del Mana said:

I am quite unclear as to how the knight may gallop backward five steps at a time, as in the stated rules, the knight's horse appears only to be able to gallop four at a time.

Ah, you're thinking of the knight actual position. What is referred here, is the starting square the knight can eliminate, not the current position of the knight and the horse.

[Tissy]

On 5/15/2020 at 1:51 AM, Demonic God said:

The easiest way, would be to move forward twice and backward once,

Isn’t it the same pattern as my last proposal?????

REPEAT:

1. move forward

2. move backward

3. move forward

[Steno]

See I like my answer 

"Well I know the mouse is going towards PC, so I just chase after it. It runs off the cliff, I stop my horse before I do. I win"

[Demonic God]

5 hours ago, Tissy said:

Isn’t it the same pattern as my last proposal?????

REPEAT:

1. move forward

2. move backward

3. move forward

the difference being that the pattern is:
REPEAT:

1. Forward
2. Forward
3. Backward
4. Forward
5. Forward
6. Backward
7. Forward
8. Forward

After 8, it cycles back to 1. That's 4 forwards in a roll