G2.2 From 1 to 100 , take a pair of integers (repetitions allowed) so that their sum is greater than 100 . How many ways are there to pick such pairs?
$$
\begin{array}{l}
(1,100),(2,100), \ldots,(100,100)(100 \text { pairs }) \\
(2,99), \ldots,(99,99)(98 \text { pairs }) \\
(3,98), \ldots,(98,98)(96 \text { pairs }) \\
\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \\
(49,52),(50,52),(51,52),(52,52)(4 \text { pairs }) \\
(50,51),(51,51)(2 \text { pairs })
\end{array}
$$

Total number of pairs $=2+4+\ldots+100=\frac{2+100}{2} \times 50=2550$
Remark: the original version was ..."take a pair of numbers"...從1到100選取兩數...
There are infinitely many ways if the numbers are not confined to be integers.