Jump to content

Of knight and mouse

Recommended Posts

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 by Demonic God
Link to comment
Share on other sites

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? 


Link to comment
Share on other sites

*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


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

Edited by Demonic God
Link to comment
Share on other sites

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 by Ungod
Link to comment
Share on other sites

  • 3 weeks later...

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).

Link to comment
Share on other sites

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.

Link to comment
Share on other sites

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?????


1. move forward

2. move backward

3. move forward

Link to comment
Share on other sites

5 hours ago, Tissy said:

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


1. move forward

2. move backward

3. move forward

the difference being that the pattern is:

  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 :)

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.


  • Forum Statistics

    Total Topics
    Total Posts
  • Recently Browsing

    • No registered users viewing this page.
  • Upcoming Events

    No upcoming events found
  • Recent Event Reviews

  • Create New...