[ Numerical inequalities. Comparing numbers.]

Sasha wrote several two-digit numbers on the board in ascending order, and then replaced identical digits with identical letters, and different digits with different letters. He ended up with (in the same order)

$$
\text { AC, AR, YR, YK, OK, OM, UM, UZ, IZ, IA }
$$

Restore the digits.
Since all numbers are two-digit and are in ascending order, their first digits also go in ascending order, that is

$$
\mathrm{A}<\mathrm{Ya}<\mathrm{O}<\mathrm{y}<\mathrm{I}
$$

If two two-digit numbers start with the same digit, the larger one will be the one with the larger second digit. Therefore, C $<\mathrm{P}, \mathrm{P}<\mathrm{K}, \mathrm{K}<\mathrm{M}, \mathrm{M}<\mathcal{Zh}, \mathrm{Zh}<$ A. Combining all the obtained inequalities, we get the chain

It remains to note that Sasha used exactly 10 different letters, which means,

$$
C=0, P=1, K=2, M=3, \mathrm{Zh}=4, A=5, \mathrm{Ya}=6, O=7, U=8, I=9 .
$$

## Answer

$\mathrm{A}=5, \mathrm{Zh}=4, I=9, \mathrm{~K}=2, \mathrm{M}=3, O=7, \mathrm{P}=1, \mathrm{C}=0, \mathrm{Y}=8$, Ya $=6$.