Multinumber

Multinumber is a term used in discussions of numeral systems to describe a numeric string that can be interpreted in more than one base, yielding a set of distinct integer values. In this usage, the same sequence of digits functions as several numbers at once, depending on the base chosen for interpretation. The concept is useful for illustrating how base and digit choice affect value and for constructing puzzles or educational demonstrations about radix systems.

Formally, let s be a nonempty string over the digit set that includes 0–9 and letters for higher digits (for example A for 10, B for 11, and so on), interpreted in bases b such that b is greater than the largest digit value appearing in s. The value of s in base b is V_b(s) = sum of digit_i multiplied by b raised to the appropriate power. If s is valid for a range of bases B = {b_min, b_min+1, ..., b_max}, then s is a multinumber, and its value set is {V_b(s) | b in B}. Some strings may use only decimal digits, others require higher bases to be valid.

Examples help illustrate the idea. The string "10" is valid for every base b ≥ 2, and its values are V_b("10") = b, giving the set {2, 3, 4, ...}. The string "1A" uses digits 1 and A (10) and is valid for bases b ≥ 11; its values are V_b("1A") = b + 10, yielding 21, 22, 23, ... for bases 11, 12, 13, and so on.

Notes: leading zeros do not change the concept. Multinumbers are primarily educational tools to show how representation differs with base and can be used in puzzles or encoding schemes that exploit multiple interpretations of a single string.