perplexus.info :: Numbers : 129 again

129 again (Posted on 2010-09-15)

There is a four digit number such that when multiplied by a single digit produces another four digit number i.e. "ABCD"*E="FGHI " (the letters between the quotation signs designate a concatenation, not the product).

The letters represent 9 non-zero distinct digits.

Find the two existing solutions to this 9-digit problem.

No Solution Yet Submitted by Ady TZIDON

Rating: 3.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Analytical observation

| Comment 3 of 6 |

Mod 9, the three numbers must sum to 0 and the product of the first two must equal the third.

There are only 6 possibilities:

0*0=0

4*1=4

1*4=4

3*6=0

6*3=0

7*7=4

Of course, E cannot be 1 or 9, so E must be 3 or 4 or 6 or 7.

And FGHI must equal 0 or 4 (mod 9).

Posted by Steve Herman on 2010-09-15 16:03:43

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