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As 3D is 3 times 5A, and they both share a final digit, their final digit must be 5 or 0.
If it were 0, then 4A would also end zero, so 3D ends in 00. This would mean that 5A also ends 00. 2D therefore would end in 0, but then it's impossible for the sum of 2D's digits to be 19.
Hence, the final digit of 5A cannot be 0, so must be 5:
As 4A is 2 times 5A, it ends in a 0:
3D is a multiple of 3, so must be 105, 405, or 705. These would mean 5A is 35, 135, or 235 (respectively). 5A has three digits so this rules out the first option. Both other options end in 35:
4A is 2 times 5A, so must end in 70:
The sum of the digits of 2D is 19:
If 5A were 135, then 4A would be 270. But then 1D ends with 21 and its digits cannot add to 15. Therefore 5A 235:
4A is 2 times 5A and 3D is 3 times 5A:
The sum of the digits of 1D is 15:
Therefore, today's number is 997.
