4) Andrea writes the sum of two three-digit numbers with the corresponding result. Then she replaces each digit with a letter, making the same letter correspond to the same digit and using different letters for different digits. In this way, she obtains:

$\mathrm{TRE}+\mathrm{TRE}=$ SEI. Then:

(A) the letter E necessarily corresponds to an even number

(B) the letter $\mathrm{S}$ necessarily corresponds to an even number

(C) the letter $\mathrm{E}$ necessarily corresponds to an odd number greater than 4

(D) the letter $\mathrm{E}$ necessarily corresponds to an even number less than 5

(E) none of the above statements is true
4. The answer is $(\mathbf{E})$.

Since Andrea obtains TRE+TRE=SEI, and the correspondence between letters and numbers is bijective, it is deduced that the two numbers he adds are equal to the same number, which we call $N$. Let's try with some examples to show that none of the statements contained in answers (A), (B), (C), and (D) are necessarily true. Choosing $N=325$ (thus $\mathrm{E}=5$), we see that (A) and (D) are not satisfied; similarly, if $N=175$ (thus $\mathrm{S}=3$), we see that (B) is not satisfied; if $N=162$ (thus $\mathrm{E}=2$), we see that (C) is not satisfied.

[Problem proposed by A. D'Andrea]