What enormous-number problem did Archimedes explore in The Sand-Reckoner?

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Portrait of Archimedes by Giuseppe Nogari shows an elderly man with white hair and beard, holding a compass, gazing downward, set against a dark background. — Archimedes Archimedes, oil on canvas by Giuseppe Nogari, 18th century; in the Pushkin Fine Arts Museum, Moscow. Archimedes was an ancient Greek mathematician and inventor.

In his treatise The Sand-Reckoner, Archimedes explored the problem of calculating the number of grains of sand required to fill the entire universe.

To solve this, he had to overcome the limitations of the existing Greek numerical notation system. He achieved this by creating an original place-value system that utilized a base of 100,000,000, allowing him to express and manipulate such an enormous quantity.1