numerosidut

Numerosidut is a term found in puzzle literature to describe a class of natural numbers whose decimal representation can be partitioned into two nonempty, contiguous blocks in such a way that the sums of the digits in the two blocks are equal. The partition must be nontrivial, meaning both blocks contain digits and neither block is the entire number.

In practice, a number is numerosidut if there exists at least one place to cut its digit string into two parts where the sum of the digits in the left part equals the sum of the digits in the right part. Because the property depends on the decimal representation, it is inherently base-specific; numbers may be numerosidut in base 10 but not in another base.

Examples

- 22 can be split as 2 | 2, with digit sums 2 and 2.

- 1010 can be split as 10 | 10, with digit sums 1+0 and 1+0, both equal to 1.

- 1230 can be split as 12 | 30, with digit sums 1+2 and 3+0, both equal to 3.

- 1001 can be split as 10 | 01, with digit sums 1+0 and 0+1, both equal to 1.

Extensions and notes

- A single-number split is allowed only if both blocks are nonempty; multiple valid splits may exist for the same number.

- A generalization considers partitions into more than two blocks where the sums of all blocks are equal, though this is less common in discussions of numerosidut.

- The concept is primarily used for recreational puzzles rather than as a formal area of mathematical research, and there is no established theory or classification beyond the stated definition.

See also: digit sum, partition of digits, recreational number theory.