math-problem.js

// Problem: ABCDE × A = EEEEEE. Each letter is a different digit.
// Source: https://twitter.com/preshtalwalkar/status/1309643691506761728?s=20

// Equation to solve: EEEEEE / A = ABCDE
// You have to try 9 digits E and 8 digits A per E (with A neither zero nor E)

for (let E=1; E <= 9; E++) {
  for (let A=1; A <= 9; A++) {
    if (A === E) continue;
    
    const solutionNumber = (E * 111111) / A;
    if (!Number.isInteger(solutionNumber)) continue;

    const solutionString = String(solutionNumber);
    if (solutionString.length === 5
      && solutionString.startsWith(String(A))
      && solutionString.endsWith(String(E))) {
      const digitSet = new Set([...solutionString]);
      // Is each digit unique?
      if (digitSet.size === 5) {
        console.log(solutionNumber);
      }
    }
  }
}