Using the 'secret' is a common way of deriving further digits in a Sudoku - if you know the sum of digits in a row or a box has to be X, then the missing digits must sum to 45-X. In the 'Cracking The Cryptic' videos, Simon is always careful to explain this, and always prefaces it with a warning that he only tells it to his closest friends (all 400k of them).

It's a joke. The numerical value of the digits has no meaning. There is no addition in sudoku.

There is plenty of addition in modern sudoku, as visible in the example shown in the linked article featuring killer cages.

Also, using a similar trick as with the dominoes, can a certain Legend of Zelda puzzle be solved?

https://gazj.substack.com/p/python-and-the-legend-of-zelda?s...

Article doesn't contain a mathematical proof (only a brute force one), but I wrote one up. Spoilers: https://news.ycombinator.com/item?id=30639211

That's a cool puzzle! It's the same as the Bridges of Königsberg, right? If each square is a node, connected by edges to adjacent squares, then it's only solvable if there are at most two squares with an odd number of edges. Think about it like this: except for the squares where you start and finish, you must use one edge to enter and another to leave.

I guess the Zelda puzzle is different because in Königsberg you can revisit islands, just not recross bridges. But that feels like something you can finesse somehow. . . . Ah, just swap nodes & edges, right? Squares : bridges :: sides : islands. Indeed, that lines up not just the restriction but the goal too.

EDIT: Oh your second link is a much nicer solution. But still it feels like there is a relationship to Königsberg.

The Zelda puzzle isn't the same as Königsberg because in Königsberg the goal is to traverse every edge, while the Zelda puzzle doesn't care about that. Think about the rows of tiles along the edges of the room - the Zelda room has dozens of tiles with 3 edges each, but it's no problem walking across them exactly once. You enter each tile from one edge and leave by a second, and it doesn't matter if you never traverse the third edge.

Swapping nodes and edges doesn't work, because many of the Zelda nodes have 3 or 4 edges, but an edge is defined as 2 endpoints. It doesn't make sense to talk about an edge with 3 or 4 ends.

The proof of non-solution to the Zelda puzzle is a simple checkerboard argument. The room's dimensions are 13 x 9, both odd, so all the corners are the same color (call it black) and there is one more black square than white. And the prize square replaces a white square. So there are two more black squares than white squares, making the problem unsolvable, since you must always alternate visiting white and black squares. The statues are a red herring - there are two on each color and so they don't affect this proof.

Great article.

"A secret I only tell my friends" is how Simon usually introduces 1 to 9 sum to 45 when he needs that fact to explain his train of thought in Cracking the Cryptic videos.

Yes, it’s a joke. Simon discloses “the secret” in almost every video, so the joke is that it’s always presented as mysterious insider knowledge even though it’s clearly not.

> a chessboard with dominoes when the board is missing two opposite corners.

A tricker version asks what square remains (unique up to symmetry) when covering a chessboard with 21 trominoes, each of which covers 3 adjacent board squares, i.e. 1x3 or 3x1.

What does missing two opposite corners mean? Opposite to each other? Opposite to the player?

Opposite to each other. Imagine a chess board, but with the bottom-left corner and the top-right corner removed.

Either A1 and H8 or A8 and H1