Logic Masters Deutschland e.V.

Sum Of Two Squares

(Eingestellt am 17. März 2026, 11:17 Uhr von Cassinii)

A dynamic fog Sudoku exploring Fermat's theorem on the sum of two squares


THEOREM

Fermat's "Sum of Two Squares" theorem states that any odd prime number, p, can be written as the sum of the squares of two integers, A and B:

p = A² + B²

if and only if p ≡ 1 (mod 4).

This means that when divided by 4, p has a remainder of 1 (for example, if p = 13, then 13 ÷ 4 = 3 with remainder 1).

RULES

Normal Sudoku rules apply.

DYNAMIC FOG

  • The grid is covered in fog. Placing a correct digit will clear the fog in that cell, and may clear fog elsewhere.
  • No guessing is required.

SQUARES AND RECTANGLES

  • A blue square/rectangle contains an odd prime number that obeys Fermat's "Sum of Two Squares" theorem.
  • No two squares or rectangles can contain the same number.
  • Note: numbers in rectangles are read from left to right or top to bottom.

CIRCLES

  • Every square/rectangle has two circles adjacent to it (orthogonally or diagonally), connected by blue lines.
  • Circles can be connected to more than one square/rectangle.
  • These circles contain the values A and B, whose squared values sum to the prime number in their attached square/rectangle.
  • A and B are both single digit numbers.

KROPKI DOTS

  • Digits either side of a white dot are consecutive.
  • Digits either side of a black dot are in a 1:2 ratio (one is double the other).
Play the Puzzle here:

Have Fun Solving!

Lösungscode: Column 1, top to bottom.

Zuletzt geändert am 17. März 2026, 20:38 Uhr

Gelöst von pep9, StefanSch, Rab3aron, L00ping007, GorgeousNicko, PjoeterBliep, Prepared Jester, kublai, SKORP17, illegel, Joyofrandomness, Felis_Timon, jkuo7, Firebird, CrippledLamp, schnitzl, dzamie, kangaroo, MaxSmartable, MattJones, dseverus, Galc127, Julianl, mbumbee, Neonesque, RadchenkoAleksandr, Jastucreudo
Komplette Liste

Kommentare

am 10. April 2026, 21:17 Uhr von Neonesque
I love a good mathematical theorem.

am 25. März 2026, 22:39 Uhr von MattJones
Coo idea, some nice logic in there. Good fun!

am 19. März 2026, 21:36 Uhr von dzamie
That was a lot of fun! I admittedly kept worrying that I might run into a 3-digit number at some point, and only after the puzzle was over did I check to see that that would've been impossible (only 117 is reachable with single-digit squares, and 1 can't be orthogonally next to itself).

I would recommend, as a personal preference, that you not reveal the entire rest of the board in one go. Going from a lot of grey fog cells to instantly all white cells kinda flashbanged me for a moment.

am 17. März 2026, 20:38 Uhr von Cassinii
Fingers crossed

am 17. März 2026, 20:34 Uhr von Cassinii
Trying to centre the "p = A^2 + B^2" text

am 17. März 2026, 19:56 Uhr von Cassinii
Hopefully last one

am 17. März 2026, 19:52 Uhr von Cassinii
More HTML testing, sorry about the comment spam :(

am 17. März 2026, 19:47 Uhr von Cassinii
Trying to move the link!

am 17. März 2026, 19:38 Uhr von Cassinii
Testing stuff :)

am 17. März 2026, 16:05 Uhr von Prepared Jester
Very nice puzzle! I did have to grab pen and paper for a little help lol

am 17. März 2026, 14:13 Uhr von Rab3aron
Very beautiful puzzle!

am 17. März 2026, 11:38 Uhr von Cassinii
Please ignore these, I'm not changing anything!

am 17. März 2026, 11:36 Uhr von Cassinii
small changes

am 17. März 2026, 11:29 Uhr von Cassinii
text change

am 17. März 2026, 11:27 Uhr von Cassinii
Added link

Schwierigkeit:3
Bewertung:86 %
Gelöst:27 mal
Beobachtet:1 mal
ID:000RXG

Rätselkombination Rätselvariante Online-Solving-Tool

Lösung abgeben

Lösungscode:

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