Sudoku X
Sudoku X is the most natural next step after plain sudoku. All the familiar
rules are in place: every row, column and 3×3 block holds the digits 1–9
without repeats. On top of that, an X is added: both main diagonals of the
grid — from the top-left corner and from the top-right one — must also
contain the digits 1–9 with no repeats at all.

The diagonal constraint is one of the greediest in the sudoku world: any
digit placed on a diagonal instantly rules itself out along its entire
line. And the intersections of a diagonal with dense blocks are the cells
where options run out fastest — experienced players start exactly there.
Every round is generated on the fly: first a full solution is built with
the diagonals respected from the very beginning, then cells are removed —
but only so that the solution stays unique. The player never gets an
unsolvable grid.
Diagonal cells are highlighted in gold, and the lines themselves are drawn
as a cross through the whole grid — the rules are visible at first glance.
Input is tuned for phones: tap a cell, an on-screen digit pad, erase with a
single button. «Check» highlights mistakes, «Hint» places a correct digit.
Three difficulties: «Easy» to get acquainted, «Hard» — when you have to
keep the diagonals in your head all the time.