2
$\begingroup$

Magical Knight knows every Square of his Magical Kingdom. In many respects, he is like any other knight...Literary,Prime, Normal(makes same allowed chess moves).

He is people Knight . As he traverses every successive square, listens to people’s problems and offers very helpful solutions. His wisdom and skills are highly respected by king as well.

All the Knights are very economical and take only minimum required 63 moves to go thro’ each successive square and their final DESTINATION.

In the same spirit of helpfulness, he wants share some details of his journey(squares with black numbers..red is from normal Knight).

Please see picture below.

Now it is upto you to put all the pieces together and document full details of their journey.

Good Luck!!!

Hint 1:

All the knights moves are same given starting and end points..you can superimpose..literary, prime,normal, magical knights moves..you are almost there..added to that 8x8 magic square property ..key number 260 for sum of rows and columns..this lets you fill any of the gaps with few logical deductions.

enter image description here

$\endgroup$
  • $\begingroup$ Are you sure it has a solution? Maybe I am missing something, is there any relevance to the black and red colours? Or all we have to do is fill the grid from 1-64 with chess moves, visiting each cell just once? $\endgroup$ – Daniel Duque Jun 17 at 16:04
  • $\begingroup$ You need to follow three previous puzzles to understand..has unique solution with 63 moves for the Knight starting from 1 and ending in 64 $\endgroup$ – Uvc Jun 17 at 16:09
  • $\begingroup$ Can somebody add links to my Knight puzzles..I am not sure how to do it..thx $\endgroup$ – Uvc Jun 17 at 16:28
  • $\begingroup$ Daniel..click on my name Uvc underneath my page..check questions..see related puzzles..you need to understand those to solve this one $\endgroup$ – Uvc Jun 17 at 16:33
  • $\begingroup$ Another one of these? I didn't finish the last one yet :-P $\endgroup$ – Rand al'Thor Jun 17 at 18:03
2
$\begingroup$

Well, this one is much easier than the last one, with more extra clues. I did all this without looking at either Daniel Duque's answer or my previous partial answer.

Step-by-step deduction

  • 2 is a knight's move between A1 and D2, so 2=B3. Then 4 is a knight's move between D2 and A5, but not B3, so 4=C4.

  • 8 is a knight's move between D8 and E5, but not F7 (10), so 8=C6. Then 6 is a knight's move between A5 and D8, but not C6, so 6=B7.

  • It's easy to see from the corners, like before, that 12=G6 and 53=B6.

  • 36 is a knight's move between H2 and H6, so 36=G4.

  • F2,G3 are the only squares a knight's move from H1 (18), so they are 17,19 in some order. We can't get from F2 to E3 (15) in two steps, since D1 (50) and G4 (36) are taken, so F2=19 and G3=17, so F1=16 a knight's move between E3 and G3.

  • 61 is a knight's move between H5 and E2, but not G3 (17), so 61=F4. Then 63 is a knight's move between E2 and H3, but not F4, so 63=G1.

  • 38 is a knight's move from H6, but not G4 (36), F5 (40), or F7 (10), so 38=G8. Then 39 is a knight's move between G8 and F5, but not H6 (37), so 39=E7.

Now we have:

partial progress

  • There's only one empty three-step path from G6 to E3, so 13=H4 and 14=G2.

  • There's only one empty three-step path from F6 to H5, so 58=E8 and 59=G7.

  • 56 is a knight's move between C7 and F6, but not E8 (58), so 56=D5.

  • B2,C3 are the only free squares a knight's move from D1 (50), so they are 49,51 in some order. We can't get from B2 to A3 (47) in two steps, since C4 (4) is taken, so 49=C3 and 51=B2. The only squares a knight's move from B1 are A3 (47), C3 (51), D2 (3), so 48=B1.

  • There's only one empty four-step path from D6 to D4, so 42=C8 and 43=A7 and 44=B5.

  • 46 is a knight's move between D4 and A3, but not B5 (44), so 46=C2.

Now we have:

enter image description here

  • There are two possible empty four-step paths from A2 to F3, but both of them need 32=D3 and 33=E1.

  • There's only one empty five-step path from C5 to A2, so 26=D7 and 27=B8 and 28=A6 and 29=B4. Then we must have 31=C1 since B4 is taken.

  • Now the only thing left is a five-step path from E4 to C5: we must have 21=G5 and 22=H7 and 23=F8 and 24=E6.

Done!

Final solution

enter image description here

$\endgroup$
  • 3
    $\begingroup$ Don't you think it's a bit ridiculous to have to detail every step of the problem like this when all the steps are basically the same? Judging by Uvc's comment on the first answer, I assume this is what they were looking for. This would be as if you answered a sudoku with "Well, since I know 9 can't be in this row, it must be here. That tells me it can't be in this column, which means it has to be a 3, which means..." repeat ad nauseam. Is that really what a good answer looks like? $\endgroup$ – scatter Jun 17 at 19:08
  • $\begingroup$ If I asked for just the solution, you are right..lot of other people have put effort into it, following all other puzzles..I did not ask for full explanation....I was looking for answer along the lines of Rand al Thor..at least partially. $\endgroup$ – Uvc Jun 17 at 19:15
  • $\begingroup$ These puzzles were developed to bring out linked properties of knights moves with magical square properties employing sudoku like solutions with further hints being given in subsequent puzzles. $\endgroup$ – Uvc Jun 17 at 19:19
  • 1
    $\begingroup$ @scatter I find it satisfying to justify an answer properly like this, and I also prefer to read such an answer than one where the solution is just given with no proof or justification. With an answer like this one, any reader can follow the steps of the answerer for themselves, and see not only the final answer (which isn't very interesting by itself) but also how such a puzzle is solved (and surely that's why we're here, to learn about the puzzle-solving process?) $\endgroup$ – Rand al'Thor Jun 17 at 19:21
4
$\begingroup$

I am not entirely sure about what the OP means by needing knowledge from previous puzzles to understand the meaning behing the colours; nevertheless I figured a path the knight can follow though his realm:

1 48 31 50 33 16 63 18
30 51 46 3 62 19 14 35
47 2 49 32 15 34 17 64
52 29 4 45 20 61 36 13
5 44 25 56 9 40 21 60
28 53 8 41 24 57 12 37
43 6 55 26 39 10 59 22
54 27 42 7 58 23 38 11

Unfortunately there is not much I can add about how I got there, and it would be very extensive to explain all 64 squares:

In summary it was much like solving a sudoku, backtracking numbers with only one possibility, locked pairs, etc.

$\endgroup$
  • $\begingroup$ Please let me know how you figured it out..documentdetails $\endgroup$ – Uvc Jun 17 at 16:37
  • $\begingroup$ In order for you to get green check, I need to know at least partial logic how you got one particular square by ruling out the possibilities leading to final restricted choice.. $\endgroup$ – Uvc Jun 17 at 16:59

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.