Which number games are based on multiplication?

Number games based on multiplication include the following types:

• Cryptarithms: These are mathematical puzzles where digits in an arithmetic operation—such as multiplication—are replaced by letters or other symbols. The goal is to deduce the original digits by applying logical rules to the operations. A specific subset of these, where the resulting letters form meaningful words, is known as alphametics.1
• Digital Problems: These puzzles involve representing integers using a specific set of digits and allowed operations. Multiplication is frequently used in these challenges, as is the factorial operation, which is defined as the product of all positive integers less than or equal to a given number (e.g., $4!=4\times 3\times 2\times 1$).2
• Number Patterns and Curiosities: Various numerical properties involve multiplication, such as automorphic numbers, which are integers whose square ends with the original number (e.g., ${25}^2=625$). Additionally, terms in multigrades can be multiplied by the same number while maintaining the equality of the sets.3