Logic Masters Deutschland e.V.

Cartesian Sums: An introductory puzzle

(Eingestellt am 2. Dezember 2025, 23:51 Uhr von damasosos92)

This puzzle was made for the fourth round of PAC, a tournament hosted by Agent.
I will probably make more advanced puzzles with this ruleset, consider this one just a warm up.


Rules:

Cartesian Sums: For each cell in the grid consider its coordinates as shown in grey outside the grid. Shade some of the cells of the grid and write in each unshaded cell the sum of its coordinates (e.g. the cell in the coordinates [3,-5] would contain the number -2). Shaded cells cannot contain numbers.

The clues outside the grid are Japanese Sum clues. A number indicates the absolute value of the sum of the digits in a consecutive set of unshaded cells. Such sets are separated by at least one shaded cell. The clues are given in the right order and every consecutive set of unshaded cells is accounted for by Japanese Sum clues.

A single '?' represents an absolute value from 0 to 9. A '??' represents an absolute value between 10 and 99, i.e. the leading digit can't be 0. E.g. '1?' could be any number from 10 to 19 and '?4' can be 14, 24, 34, etc. A '*' represents any number of sets of consecutive unshaded cells with arbitrary sums including no unshaded cells at all.

Draw a non-intersecting, non-branching loop through the centers of all unshaded cells.

Furthermore, the grid is divided in four quadrants. In each quadrant, there is a single and distinct clue type that appears only within the boundaries of that quadrant and interacts only with the cells of its quadrant and inside the borders of its quadrant. The clue types and relative rules are as follows:

  • Top left: Turnloop clues. The loop must pass through every circle. The loop turns on every circle, and travels straight through the same amount of cells on either side.
  • Top right: Masyu with grey clues. The loop must pass through every circle. The loop must turn on black circles and travel straight through the cells on either side. The loop must go straight through white circles, and turn in at least one of the cells on either side. All the clues are grey: the solver must determine if they are white circles or black circles.
  • Bottom left: Castle wall grey clues. The loop may not enter outlined cells or cells containing clues. A clue indicates the number of line segments in the indicated direction. Vertical arrows only count vertical lines, and horizontal arrows only count horizontal lines.
  • Bottom right: Midloop clues. The loop must pass through every square. Each square marks the center of a straight line segment it lies on.


Solve on Penpa+




An example of the ruleset with a smaller grid is provided in the image below:



Have fun solving and please leave a comment after your solve!

Lösungscode: Column -3, from top to bottom (16 letters): put the letter X for a shaded cell, the letter T for a turn of the loop and the letter S for a straight piece of the loop. Es. XXXTTTTSSTSXXSSX


Gelöst von sfushidahardy, tuturitu, Nell Gwyn, Christounet, Agent, moss, MaizeGator, nuzzopa, Playmaker6174, puzzler05, Grausbert, dumediat, aqjhs, yttrio, ddx02, ns08, anomime, Nensche777, Bellsita, isajo4002, kays
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Kommentare

am 30. Dezember 2025, 11:46 Uhr von Nensche777
This was really fun, thanks! Looking forward to possibly more puzzles of this type!

am 13. Dezember 2025, 18:31 Uhr von yttrio
Very cool logic from the Cartesian sums idea, and I'm always a sucker for a good loop puzzle!

am 12. Dezember 2025, 22:47 Uhr von dumediat
I really loved this idea, and the use of the absolute values of cells turned what could have been a tedious solve into a really smooth and enjoyable one!

am 8. Dezember 2025, 12:47 Uhr von Playmaker6174
Very original concept and a great fun (and surprisingly not too tricky) solve here! I’m a sucker for some funny arithmetic works there x)

am 3. Dezember 2025, 16:40 Uhr von Agent
Cool concept and great execution!

am 3. Dezember 2025, 07:05 Uhr von Christounet
Original idea and very funny how this works! Thanks :)

am 3. Dezember 2025, 00:01 Uhr von sfushidahardy
Fun puzzle!

Schwierigkeit:4
Bewertung:97 %
Gelöst:21 mal
Beobachtet:1 mal
ID:000QE8

Variantenkombination Neu Online-Solving-Tool Groß Wegerätsel Färberätsel

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Lösungscode:

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