A numerical digit is one symbol in a positional notation string, denoting an integer from zero through one less than the radix.
A positive integer whose first decimal numerical digits have the same sum as its last digits, where is the number of digits. For odd , the shared middle digit cancels from the equality. Counts and value sums can therefore be assembled from two half-length digit dynamic programming tables indexed by base-p digit sum.
A positive integer whose adjacent decimal numerical digits differ by exactly 1. Its digits form a walk on the path graph , with a nonzero starting digit. Counting pandigital numbers of this type can use digit dynamic programming with the final digit and a bit mask of visited digits as the state.
Repeatedly sum the numerical digits of a nonnegative integer in base until a single numerical digit remains. For , the result is , while the result for zero is zero. This follows because , so summing numerical digits preserves the integer congruence class modulo .
A number whose representation contains every numerical digit from a specified alphabet. The convention must specify the base, whether zero is required, and whether repetitions are allowed. In many counting problems, “0-to-9 pandigital” means that all ten decimal numerical digits occur exactly once; other problems require only that each occur at least once.
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A numerical digit is a symbol used to represent numbers in a numeral system. In the most commonly used base-10 (decimal) system, the digits are the ten symbols from 0 to 9. Each digit has a specific value depending on its position within a number. For example, in the number 253, the digits are 2, 5, and 3. Here: - The digit 2 represents 200 (2 x 100).