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 Find just one digit (Posted on 2005-11-10)
If ABC+DEF+GHI=JJJ, each letter stands for a different digit, and no number starts with zero, what is J?

 See The Solution Submitted by Federico Kereki Rating: 3.8000 (5 votes)

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 Another method. | Comment 5 of 13 |

The digital root of the numbers 0-9 is 9.

If j is 1, the digital root on the right is 3, and on the left is 9-1=8, which don't match.

If j is 2, the digital root on the right is 6, and on the left is 9-2=7, which don't match.

If j is 3, the digital root on the right is 9, and on the left is 9-3=6, which don't match.

If j is 4, the digital root on the right is 3, and on the left is 9-4=5, which don't match.

If j is 5, the digital root on the right is 6, and on the left is 9-5=4, which don't match.

If j is 6, the digital root on the right is 9, and on the left is 9-6=3, which don't match.

If j is 7, the digital root on the right is 3, and on the left is 9-7=2, which don't match.

If j is 8, the digital root on the right is 6, and on the left is 9-8=1, which don't match.

If j is 9, the digital root on the right is 9, and on the left is 9-9=0 --> 9, which matches.

So j is 9.

 Posted by Charlie on 2005-11-10 09:37:55

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