Adam's puzzle, the puzzle from Adam, the puzzle made specifically by Adam, that puzzle.

adam_puzzle.js

const toNum = digits => Number.parseInt(digits.join(''))
const valid = digits => toNum(digits) % digits.length === 0

function solve(digits = []) {
  if (digits.length === 9) { return toNum([...digits, 0]) }
	for(var i = 1; i <= 9; i++) {
  	if (digits.indexOf(i) >= 0) { continue }
    if (valid([...digits, i])) {
    	const soln = solve([...digits, i])
      if (soln) { return soln }
    }
  }
}

document.write(solve())