### Hamle Sudoku by Prasanna Seshadri

or solve online (using our beta test of Penpa-Edit tools; use tab to alternate between Sudoku number entry mode and a shading mode to mark the top grid.)

**Theme:** Clue Symmetry and Logic

**Author/Opus:** This is the 17th puzzle from our contributing puzzlemaster Prasanna Seshadri.

**Rules:** Variation of Sudoku rules. Each number in the top grid must be moved either up, down, left, or right the same number of cells as that number’s value without crossing the border of the grid. Numbers must all land on unique spots, but unlike in normal Hamle numbers may be adjacent after moving and white areas may not all be connected. Then solve the resulting sudoku. (Note: It is possible for a number to have two valid movement options in the solution; it is only required that at least one direction of movement exists for each number.)

**Answer String:** Enter the 2nd row from left to right, followed by a comma, followed by the 5th row from left to right.

**Time Standards (highlight to view):** Grandmaster = 9:30, Master = 15:00, Expert = 30:00

**Solution:** PDF

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I don’t entirely understand what you’re trying to say in the parenthetical. Are you just saying that the final grid is a unique solution, but there may be more than one set of movements that lead to that unique solution?

For example, looking at the 2 in R9C4, is the point that it’s possible that there is a 2 in the new grid at both R9C2 and R7C4, not that there are two different solution grids depending on how you move the two?

Yes, that’s what it means. The number must be moved in at least one direction, it can also exist in multiple directions away from itself (but with Sudoku restrictions, only two directions at most are possible).

Can an example link be provided for this sudoku?I don’t understand the rules.

Here’s one that is hopefully clear enough, if I understand the rules correctly. Top-left is the puzzle, bottom-right is the solution. The other two grids are the Hamle step.

Thanks for posting that image.

Thank You.i)So if a number is displaced it can be displaced throughout in only one direction .ii)Also the cell in which the number is initially present cannot be visited by that again. i.e., considering for instance the 4 in R1C3 ,it cannot be moved in this way R1C3–R2C3–R1C3–R2C3–R3C3.

I am sorry .Looking at my comment again I realized that the thing I had stated in ii) won’t come into the picture at all as it violates what had been stated in i)(direction change)

Nope, the movement has to be straight. The resultant solution must have the number in at least one direction at that distance away from it.

Here’s another, just to emphasize the rule Andrew needed to confirm (check the R2C3 clue and the multiple 1s around it in the solution)

39 min

Clearly stumbled trying to complete this.After deducing n bar va E4P4, for some reason I failed to notice that the bar tvira va E4P8 pna trg vagb E3P9 gbb ohg V xrcg chggvat vg va E5P9 .Obviously the sbhe above that is the culprit.

Ng gur svany zbzragf jnfgrq fbzr gvzr ntnva guvaxvat jurgure gb zbir gur 5 va E9P9 hc be gb gur yrsg naq ortna gb qbhog vs gur chmmyr vf havdhr hagvy V ernyvmrq gung gur fbyhgvba vf gur fnzr ertneqyrff bs gur qverpgvba!

Nice Innovative sudoku variant.

As you made it a point to note that one standard Hamle rule is no longer in effect, is the other rule where all white cells (or in this case, unclued cells as they will be filled for Sudoku purposes) must form a single area after moving also no longer in effect? It’s just a bit weird to make a case of removing one rule, but not addressing the other.

Yeah, the single area rule isn’t in effect either. I think this was just missed out unintentionally.

I apologize for this; it was in Prasanna’s original rules but he submitted two forms of the puzzle and I probably lost it in the shuffle.

Honestly, calling this a Hamle Sudoku might have been an unnecessary choice as two of the three primary Hamle rules aren’t used.

Well, I understood instantly what the idea was by the name Hamle and that we had to move the digits. So I think that’s why it’s a good choice of name. I just thought it unnecessary to mention the other rule was not in effect.

Personally I believe the movable clues is a more prominent rule for Hamle as there are so many types where the other two rules apply (Hitori, Heyawake, Compass, Yajisan Kazusan, etc.). The variant itself was inspired from Hamle. Also, Movable Digits was already taken as a name for a similar variant, so I decided not to go with something generic.

I made my comment because “Hamle” is not a puzzle we have ever posted here; I dislike having contingencies to rules many of our solvers may not know.

But I agree 100% that Hamle evokes the right thinking if you do know what it is. That is why I kept your proposed name but I was 60:40 on it to be honest.

Puzzle of the year so far, really enjoyed this, keep up the great work!

That was very impressive !

I didn’t understand the significance of Andrews question until I had to move the final clue (gur svir va gur obggbz evtug pbeare).

Gung punva bs svir/avar uvqqra cnvef unq zr chmmyrq sbe n frpbaq gung gur chmmyr zvtug abg or havdhr orsber gur svany vafvtug uvg zr !

As Thomas has mentioned above, there were originally two forms of this puzzle. I was unsure right from the time I first thought of this variant, what to do with the potential ambiguities that might arise, fb V tnir Gubznf gjb bcgvbaf, rnpu bs juvpu jnf ohvyg gb raq jvgu qrnyvat jvgu gur nzovthvgl va n qvssrerag jnl, fb V pbhyq erfbyir gur ehyrf nf n fgnaqneq sbe shgher hfr. Gur raq erfhyg V qrfverq jnf gb unir na vagebqhpgvba gb gur glcr gung hfrf nyy gur ehyrf arprffnel, ohg V jnfa’g fher lrg nobhg juvpu frg bs ehyrf gb hfr! Thomas’ feedback was really helpful here in picking the right one.

Probably my favorite puzzle this year (so far). Great ending as hagriddler described.

Great puzzle. Even better, this is also an excellent “Knapp-daneben-Sudoku” (i.e., move every clue by 1 instead of the clue value). Add clues r4c4=7 and r6c6=6 to make it unique, but it’s a beautiful tricky solve for quite a while even without those. Don’t ask.