Hi,

tarek!

Thank you very much for this thread! I tried "King's tour" - it is nice puzzle with great possibilities for player's analisys. It is more interesting even than sudoku in some aspects. Separate Universe being not so carefully discovered as sudoku.

It turns out that "King's tour" is a kind of Hidato puzzle (thanks to

dyitto for his clarification) with minor differences. Wikipedia says: "Hidato is a logic puzzle game invented by Dr. Gyora Benedek, an Israeli mathematician". But when was it invented? I assume Hidato was invented in 2008, is it so? Maybe

dyitto has more accurate information about it?

Sudoku and Hidato have many common properties, and at least some sudoku solving methods can be used for Hidato solving (for example, naked and hidded pairs, trios, etc.). Hidato has even its own unavoidable sets. Maybe it is not so curious, because both puzzles are kinds of number permutation puzzles with constraints.

I wrote a solver to verify King's tour puzzles posted by youself. When I coded my solver ("smart" backtracking solver, it finds naked and hidded singles, otherwise - backtracks (T & E)), I discovered that "candidate finding" phase for King's tour is not trivial and is more complicated than for sudoku. It seems to me "Pencilmark style" manual solving of King's tour is possible but not feasible (at least, for hard puzzles), because the same cell can be occupied by huge number of candidates (up to 64 per cell).

tarek wrote:These 8x8 (Chess board) puzzles have been verified to be minimal and to have a unique solution by my solver, I couldn't find an independent solver to verify this.

here is a sample open King's tour puzzle & solution

- Code: Select all
`22 21 00 00 27 00 63 00 `

00 00 00 01 00 00 00 00

38 00 00 00 00 00 00 00

00 00 00 11 00 00 00 00

49 00 00 00 00 00 00 00

00 00 00 00 00 13 58 00

45 00 00 00 00 33 00 00

00 00 00 00 00 00 00 00

22 21 25 26 27 03 63 64

23 24 20 01 02 28 04 62

38 09 10 19 18 05 29 61

39 37 08 11 06 17 30 60

49 40 36 07 12 31 16 59

48 50 41 35 32 13 58 15

45 47 51 42 34 33 14 57

46 44 43 52 53 54 55 56

I confirm that this puzzle has unique solution. My solver solved it in 0.02 sec. But it is not minimal. You can delete moves 21, 22 and 58 (only one move can be deleted at once), and the puzzle will still have unique solution. (But no additional move removals are possible.)

Then I tried to solve other posted King's tour puzzles. All puzzle, except Puzzle 6, have unique solutions. Here is strange Puzzle 6, containing 9 rows and duplicated moves ("01" and "64").

tarek wrote:- Code: Select all
`60 61 19 63 64 01 35 34 `

00 18 09 10 00 00 13 28

00 00 00 00 11 12 00 00

00 00 00 00 00 00 01 00

00 00 00 00 00 00 00 49

00 00 00 00 00 00 00 00

00 00 00 44 04 51 00 00

00 00 00 00 00 00 00 00

64 00 00 42 00 00 00 00

Serg