Sandwich numbers

We define a sandwich number as a natural number $n$ with only two different digits $d$ and $e$ , forming a sequence $de_1e_2\cdots e_kd$ . That is, the digit $d$ is the first and last digit of $n$ (it’s the bread), and the digit $e$ is repeated $k \geq 1$ times in between the two $d$ digits (it’s the filling). For example, 121 is a sandwich number with $d = 1$ , $e = 2$ , and $k = 1$ . And 4004 is a sandwich number with $d = 4$ , $e = 0$ and $k = 2$ .

More examples of sandwich numbers: 7227, 41114, 966669, 10001, and 535.
Examples of numbers that are not sandwich numbers: 9, 12, 113311, 7878, 1234, 9991, 1000.

Implement a function is_sandwich that receives a natural number and returns true if it is a sandwich number and false otherwise.

The function header should be:

/**
 * @pre  n >= 0
 * @post returns true if n is a sandwich number, false otherwise
 */
bool is_sandwich(int n);

Observation

You only need to submit the requested function; the main program will be ignored.

Problem information

Author: PRO1

Generation: 2026-01-25T13:08:44.766Z