An amphoteric oxide is one that displays both acidic and basic properties; such substances react with both acids and bases. In the p-block, several elements can form amphoteric oxides, particularly those elements that are metallic or metalloid in nature. It's essential to recognize which oxides among the provided list have an amphoteric character:

$\mathrm{Cl}_2 \mathrm{O}_7$ - This is dichlorine heptoxide, an oxide of chlorine, and shows acidic properties. It is not amphoteric.
$\mathrm{CO}$ - Carbon monoxide does not behave as an acidic or basic oxide; it is mainly a neutral oxide.
$\mathrm{PbO}_2$ - Lead(IV) oxide, also known as plumbic oxide. This oxide of lead is amphoteric, but it is much less common and less amphoteric than lead(II) oxide, PbO.
$\mathrm{N}_2 \mathrm{O}$ - Nitrous oxide is a neutral oxide; it does not exhibit acidic or basic properties.
$\mathrm{NO}$ - Nitric oxide, like N2O, is a neutral oxide.
$\mathrm{Al}_2 \mathrm{O}_3$ - Aluminium oxide is well known for being amphoteric. It reacts with both acids and bases to produce salts and water.
$\mathrm{SiO}_2$ - Silicon dioxide is generally acidic. Although it does not react with water to form an acidic solution, it will react with basic oxides. Therefore, it is typically not considered amphoteric.
$\mathrm{N}_2 \mathrm{O}_5$ - Dinitrogen pentoxide is an acidic oxide; it is the anhydride of nitric acid.
$\mathrm{SnO}_2$ - Tin dioxide, also known as stannic oxide. This oxide of tin is amphoteric, reacting with both acids and bases.

From the list, the amphoteric oxides are:

$\mathrm{PbO}_2$ - Lead(IV) oxide (less commonly amphoteric compared to PbO)
$\mathrm{Al}_2 \mathrm{O}_3$ - Aluminium oxide
$\mathrm{SnO}_2$ - Tin dioxide

So, the number of amphoteric oxides in the list provided is 3.