Full house
A unit with one empty cell takes the only missing value
How to use it
The cheapest deduction in the game: count a line. Scan each row and each column, on the letter layer and on the digit layer separately, for a unit with exactly one empty cell. Whatever symbol that line still misses goes in the empty cell — there is nowhere else it could hide.
Check for full houses after every placement: filling one cell often completes a line and creates the next full house. The two layers are counted separately — the Latin rules never mix digits into letters — so a row can be complete in letters while still missing one digit: remember to count both halves.
Why it is sound
A row or column of a valid Eulero grid is a permutation of the alphabet: every letter exactly once and every digit exactly once. A unit missing exactly one symbol has no freedom — each of its completions places the missing symbol in the only empty cell.
A worked example
Row 4 already shows A, C and D in its letter layer; the single empty cell, r4c3, is the only place the missing letter B can go. Count the line, place B, and its column-3 peer loses its B — after which the grid unwinds by singles. Full houses like this one are the moves you make without slowing down: scan the nearly-complete rows and columns first, on each layer separately.