Normal Knight is savvy, energy saving as he travels through Regular Country... Ride along and Document Details of his Journey

As this Knight (only chess move allowed) journeys through , he takes minimum (63) of hops to reach his destination of 64 starting from 1. He makes a pit stop at every successively numbered site. No cell is ever revisited.

He is very helpful Knight. Unlike Prime Knight, he is willing to give you more details of his journey. The numbered cells shown in the picture are mandatory stops.

Just like him, you always should see big picture and figure out the rest of the steps of his economical journey.

enter image description here


Step-by-step deductions (partial)

  • From any corner there are only two possible knight's moves. So G6=12 and B6=53 and F2,G3 must be 17,19 in some order.

  • From D1 (50) we can't move to E3 (15) or F2 (17,19), so B2,C3 must be 49,51 in some order.
    Then from A2 (30) we can't move to C3 (49,51), so C1,B4 must be 29,31 in some order.

  • The only options for 2 are C2,B3. So 4 can't be in B3, and (since B4 is 29,31) 4 can't be in C6 either. So C4=4.

  • From A4 we can only reach B6 (53), C5 (25), or B2,C3 (49,51). So A4=52.

  • From H2 (35) we can only reach F1,F3,G4. So two of these three must be 34,36. Also 16 is between E3 (15) and one of F2,G3 (17,19), so it must be in one of F1,G4. So F1,F3,G4 are 16,34,36 in some order.

  • From B1 we can only reach C3 (49,51) or D2,C3 (one of which must be 3). So B1=48, which means C3=49 and B2=51 and D2,A3 are 3,47 in some order.

  • From B3 we can only reach A1 (1), A5 (5), C1 (29,31), C5 (25), D2 (3,47), or D4 (45). So this square must be one of 2,46.

  • From F1 we can only reach D2 (3,47), E3 (15), G3 (17,19), or H2 (35). So in the end this square can't be 34 or 36: we have F1=16, hence G3=17 and F2=19.

Filled grid (partial)

enter image description here

(A big number means that number is definitely in that square. Two or three small numbers means that square must contain one of those numbers: e.g. G1 must be either 33 or 63, although either 33 or 63 might also be elsewhere. A number with a question mark means that square is one of only a few possibilities for that number: e.g. 13 must be in F4 or E7, although either of those squares might also be another number.)

Here I can't see any more immediate deductions to make, so I'm going to try a "what-if".

| improve this answer | |
  • $\begingroup$ Couldn't 63 be in F4 or G5 as well? $\endgroup$ – TheSimpliFire Jun 16 '19 at 13:45
  • $\begingroup$ @TheSimpliFire F2 as well $\endgroup$ – SteveV Jun 16 '19 at 14:10
  • $\begingroup$ As I see it, G1,F2, F4, G5 are all possibilities $\endgroup$ – Uvc Jun 16 '19 at 14:23
  • $\begingroup$ If you look at big picture, you have lot more clues than you think $\endgroup$ – Uvc Jun 16 '19 at 14:24
  • $\begingroup$ Anyway, Magical Knight will be coming tomorrow morning to dispense his wisdom for efficient navigation and even more clues $\endgroup$ – Uvc Jun 16 '19 at 14:26

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