Nt... again

Math Junior
1

Find all four-digit numbers ABCD such that:

  1. The number itself ABCD is divisible by 9.
  2. If the number is reversed to DCBA, the new number is divisible by 11.
  3. The sum of the digits A + B + C + D is divisible by 5.
  4. All digits are distinct and none of them is zero.
2

الحل

There is no number that applies this condition because divisibility by 9 A+B+C+D produces a number that is divisible by nine and divisible by five, and five and nine are relatively prime, so it is assumed that A+B+C+D/45, and this is impossible because their maximum result = 36, and this is if they are all = 9, which is the greatest possibility, so it is impossible for there to be a number that applies this condition