The original X-Sums rule, that forms the basis of this genre, can be traced back to the [SUDOKU 8X8 LMI contest|https://logicmastersindia.com/lmitests/?test=M201205S], by @ZuzanaHromcová & @MatúšDemiger. This was followed shortly by two addtitional puzzles: [one|https://puzzleparasite.blogspot.com/2012/05/puzzle-103-x-sums-sudoku.html] by @BramDeLaat and [another|https://logic-masters.de/Raetselportal/Raetsel/zeigen.php?id=0001F7] by @RichardStolk. 

In 2020, @JonasGleim made a [x-sums] puzzle for the [Puzzle Alphabet competition|https://logic-masters.de/Wettbewerbe/CE/wettbewerb.php?id=147], which is likely the first standalone [x-sums] puzzle.

In 2022, @dohz formed the first full [x-sums] puzzle set. Inspired by this [#classic] set, site.author added arrows plus some extra [#cursed] puzzles, while creating this interactive app (2023), using the [Kudamono Editor].

Each puzzle has a single, unique solution.


## Classic [x-sums] puzzles
### by @dohz

W=5x5&L=(3)2(4)3(4)6(2)2(2)6&LEX=(3)r2(1)r3(1)d3(5)u7(5)l3&A=dohz&T=Falling_in_Sequence&G=x-sums
W=5x5&LEX=(6)r5(6)d3(6)d2(10)u3(10)u2(10)l3&A=dohz&T=Inside_Joke&G=x-sums
W=5x5&LEX=(20)e0(5)s6(15)n11(10)w6&A=dohz&T=Step_Counter&G=x-sums
W=5x5&LEX=(6)e0(12)r3(12)u6(6)d5(6)l6(12)w3&A=dohz&T=Seeing_Double&G=x-sums
W=6x6&LEX=(14)r2(14)r2(12)d7(15)u1(12)d3(15)u1(13)l7(13)l2&A=dohz&T=Consecutive_Pairs&G=x-sums
W=6x6&LEX=(10)e0(17)r3(17)r2(10)d6(17)d6(17)n3(10)l3(10)l2&A=dohz&T=Archway&G=x-sums
W=6x6&LEX=(12)e0(8)r3(8)s4(8)d6(12)u1(12)n6(12)l4(8)w3&A=dohz&T=Stormy_Night&D=2023-04-15&G=x-sums
W=7x7&L=(7)0(6)21(5)7(4)16(3)1(2)3&LEX=(8)r2(9)r2(10)r2(11)d6(12)d4(1)d4&A=dohz&T=Smushed_Clock&G=x-sums
W=7x7&LEX=(11)e0(1)r3(13)r3(3)d6(5)u1(15)d5(17)u1(7)l6(19)l3(9)w3&A=dohz&T=Odds&G=x-sums
W=7x7&LEX=(15)r2(15)r2(15)s4(15)d2(15)u5(15)u2(15)d3(15)n3(15)l3(15)l2&A=dohz&T=Fifteens&G=x-sums
W=7x7&LEX=(17)e0(18)r3(9)r2(8)u8(8)d1(14)u3(14)d1(18)l8(9)l2(17)w3&G=x-sums&A=dohz&T=Mirror_Match&D=2024-01-30
W=7x7&LEX=(14)r3(14)r3(9)u5(8)d1(23)u1(18)d1(9)u3(8)d1(23)u1(18)d1(19)l5(19)l3&A=dohz&T=Twin_Convention&G=x-sums

### @PinkHoodie

This small example by @PinkHoodie clarifies the behaviour of absent cells:
W=3x3&L=x4x2&LEX=(5)7(3)5&LEX-AL=s12&LEX-AU=s7&LF=(1)0(3)1(2)1(2)1(3)2(2)2(1)1&G=x-sums&A=PinkHoodie&D=2025-02-09&F=1&T=X_Gap



## Cursed

### by site.author
This series uses empty arrows inside the board, thereby giving no number clue away. It can be considered a small //cursed// expansion to the original, //classic// ruleset, which did not bar this possibility.

W=2x2&LF=(1)0(2)1(2)1(1)1&L=e0w3&G=x-sums&A=Pedro&D=2023-04-12&N=138
W=3x3&LF=(1)0(2)1(3)1(3)1(1)1(2)1(2)1(3)1(1)1&L=e0d2&G=x-sums&A=Pedro&D=2023-04-12&N=139
W=4x4&LF=(3)0(1)1(4)1(2)1(4)1(3)1(2)1(1)1(2)1(4)1(1)1(3)1(1)1(2)1(3)1(4)1&L=s7n2d5&G=x-sums&A=Pedro&D=2023-04-12&N=140
W=5x5&LF=(1)0(2)1(3)1(4)1(5)1(3)1(4)1(5)1(1)1(2)1(4)1(5)1(1)1(2)1(3)1(2)1(3)1(4)1(5)1(1)1(5)1(1)1(2)1(3)1(4)1&L=d2r2n8d2n3n3&G=x-sums&A=Pedro&D=2023-04-12&N=141
W=6x6&LF=(4)0(3)1(6)1(5)1(1)1(2)1(1)1(4)1(3)1(6)1(2)1(5)1(5)1(1)1(2)1(4)1(6)1(3)1(6)1(5)1(1)1(2)1(3)1(4)1(3)1(2)1(5)1(1)1(4)1(6)1(2)1(6)1(4)1(3)1(5)1(1)1&L=r2e4e1r1e5n2e3d4d4w1w1&G=x-sums&A=Pedro&D=2023-04-13&N=142
W=7x7&LF=(7)0(1)1(3)1(2)1(5)1(6)1(4)1(1)1(4)1(6)1(3)1(7)1(2)1(5)1(3)1(5)1(2)1(1)1(6)1(4)1(7)1(6)1(3)1(5)1(2)2(7)1(1)1(5)1(7)1(4)1(6)1(1)1(3)1(2)1(4)1(2)1(7)1(5)1(3)1(1)1(6)1(2)1(6)1(1)1(7)1(4)1(5)1(3)1&L=s1d3r1u6n7w2(4)4s6n1e1n13&G=x-sums&A=Pedro&D=2023-04-15&K=dohz&N=143
W=8x8&LF=(2)0(4)1(7)1(1)1(6)1(8)1(5)1(4)2(8)1(1)1(6)1(2)1(7)1(3)1(5)1(5)1(7)1(6)1(2)1(8)delrsu1(3)1(1)1(4)1(6)1(5)1(8)1(4)1(3)1(2)1(7)1(1)1(8)1(3)1(2)1(5)d1(1)1(4)1(6)1(7)s1(3)1(1)1(5)1(7)w1(4)1(6)1(2)1(8)d1(1)1(2)1(4)1(3)1(7)1(5)1(8)l1(6)w1(7)n1(6)1(3)1(8)1(5)1(1)1(4)1(2)1&L=s3(3)4r4delrsu9d15s4w4d4l7w1n1&G=x-sums&A=Pedro&D=2023-04-14&N=144&T=Almost_there

### by 5381
W=5x5&L=s2d10l2l6&LEX=ey0ry1ry1ry1ry1ry1sy1uy1dy1uy1dy1uy1dy1uy1dy1uy1dy1ny1ly1ly1ly1ly1wy1wy1&G=x-sums&A=5381&D=2024-03-10&F=3&T=Abstract


### Bonus questions
In addition, here's some bonus questions (idea by @dohz):

W=3x2&LF=(1)0(2)1(2)1(3)1(3)1(1)1&LEX=sy2dy3ny6&G=x-sums&A=Pedro&D=2023-04-13&N=145
W=3x4&LF=(2)0(4)1(1)1(3)1(1)1(3)1(4)1(2)1(4)1(2)1(3)1(1)1&LEX=ry1ey1ry1ry1ey2sy1sy2ly6&G=x-sums&A=Pedro&D=2023-04-13&N=146

## Variants

### ´´zero´´
V=zero

The ´´zero´´ variant was first used in a standalone [X-sums] puzzle by @JeffreyBardon.

Here's a set of puzzles by @dohz using this variant:

W=5x5&LEX=(4)r2(2)d8(5)u3(3)l8&V=zero&G=x-sums&A=dohz&T=Consecutives
W=6x6&LEX=(8)r3(8)r2(8)u7(7)d1(8)u1(7)d1(7)l7(7)l2&V=zero&G=x-sums&A=dohz&T=Parley
W=6x6&LEX=(12)r1(12)r2(12)r2(7)d6(7)d4(6)u1(7)d3(14)l3&V=zero&G=x-sums&A=dohz&T=The_Wedding
W=7x7&LEX=(17)r3(17)r1(17)r1(14)u6(14)u2(7)d1(14)u1(7)d1(7)d2(1)u3(1)n2(1)l1(8)l3(8)l1(8)l1&V=zero&G=x-sums&A=dohz&T=Trips

And a puzzle by @PinkHoodie:

W=4x4&LEX=(4)6(3)4(1)5(2)2&LEX-AL=s15s2&LEX-AU=s6s4&LF=(3)0(0)1(1)1(2)1(0)1(2)1(3)1(1)1(2)1(1)1(0)1(3)1(1)1(3)1(2)1(0)1&G=x-sums&V=zero&A=PinkHoodie&D=2024-05-24&F=2&N=1&O=Zero&T=Invlaid

### ´´kropki,clues-missing´´
V=kropki,clues-missing

W=3x3&LEX-AD=s8s2&LEX-AU=s5s2&LEX-KROPKI=b6w3&L-RING=s0s1s1s1s1s1s1s1s1&LEX-RING=s5s2s1s2&LF=(3)0(2)1(1)1(2)1(1)1(3)1(1)1(3)1(2)1&LFEX=(6)5(3)2(6)1(5)2&G=x-sums&V=kropki,clues-missing&A=PinkHoodie&D=2024-05-24&F=1&N=1&O=Clues_Missing_+_Kropki&T=KropSum

### ´´antiknight´´
W=6x6&LEX=(18)2(6)9(9)5(6)9&LEX-AD=s11&LEX-AL=s25&LEX-AR=s2&LEX-AU=s16&LF=(6)0(5)1(2)1(4)1(3)1(1)1(5)1(6)1(4)1(2)1(1)1(3)1(2)1(4)1(3)1(1)1(5)1(6)1(4)1(2)1(1)1(3)1(6)1(5)1(3)1(1)1(5)1(6)1(4)1(2)1(1)1(3)1(6)1(5)1(2)1(4)1&G=x-sums&V=antiknight&A=PinkHoodie&D=2024-06-02&F=3&O=Antiknight&T=Xnight_Sums

## Acknowledgements and Changes

**2023-04-13** Extensive thanks to @dohz for transcribing the [#classic] set (and adding a new puzzle!), for thoroughly checking the [#cursed] set!
**2023-04-15** Thanks to @dohz for making this page and implementation tremendously better!
**2023-04-16** Thanks to @FreddieHand, @JonasGleim, @XSheep, @MartinEnder, @djmathman, @IHNN, @TomCollyer for help tracing and understanding the elusive origins of this genre.
**2023-11-04** Fixed a regression found by @dohz (cause: incorrectly set mode at startup)
**2023-11-05** Restored correct grid/frame drawing (external lines no longer shown); added slightly better hotkeys for arrows
**2024-01-20** Variant ´´zero´´ added to X-sums
**2024-01-23** @dohz transcribed 4 puzzles using the newly implemented ´´zero´´ variant! Thank you.
**2024-01-30** Puzzle //Mirror match// by @dohz was updated to a stronger version
**2024-01-12** [X-sums] error style updgraded alongside that of [Hit Points]
**2024-03-10** A cursed puzzle was sent by @5381 - thank you!
**2024-03-19** @PinkHoodie [modernised|../panels#modern] the rule panels for [x-sums], a tricky task. Thank you!
**2024-05-24** The particular case of ´´kropki´´ clues outside the grid is now supported, for an X-sums puzzle by @PinkHoodie.
**2024-05-24** :::puzzletters @PinkHoodie sent 2 puzzles using variants ´´kropki,clues-missing´´ and ´´zero´´!
**2024-06-03** The ´´antiknight´´ variant now considers only inside numbers, as highlighted by @PinkHoodie by sending a great test case, and a puzzle!
**2025-01-14** External arrows became optional in [X-sums], when axis-aligned, following the global convention for all genres. Highlighting style updated accordingly.
**2025-02-10** A small example by @PinkHoodie clarifying the behaviour of absent tiles was added - thank you!
**2025-03-01** A bug in the external clue range reported by @Pinkhoodie was patched. Also, @PinkHoodie recently re-added missing arrows to the variant puzzles.