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The authentication method that requires users to input a numeric code they have memorized is the Personal Identification Number (PIN). A PIN is a specific numeric string that is user-defined and must be remembered by the user. It is often used in conjunction with a physical card or device for additional layers of security. Because it is straightforward and easy to use, it is a common method for securing access to various systems, including banking services and mobile devices.

In contrast, token authentication typically involves a physical device or software application that generates a one-time code, thus not relying on the user's memory of a numeric code. Multi-factor authentication adds layers of security using multiple methods (such as a password and a biometric scan) rather than relying solely on a memorized number. Smart card authentication utilizes a physical card that contains electronic data, which the user must have on hand rather than simply remembering a number.