Let's determine the value of the following expression:

$$
100^{2}-99^{2}+98^{2}-97^{2}+\ldots+2^{2}-1^{2}
$$
The given expression can also be written as:

$$
(100+99)(100-99)+(98+97)(98-97)+\ldots(2+1)(2-1)
$$

or

$$
100+99+98+97+\ldots+2+1
$$

The sum of this arithmetic series is

$$
50(1+100)=5050
$$

(Vilmos Erdös, Budapest.)

Number of solutions: 54.