In a certain multiplication sample all the digits were replaced by their mod 3 value (e.g. 875 became 212),rendering:
1202*102=222210
Please restore the original sample and either show that there are no others or provide extra solutions.

I started trying to solve this analytically but it seemed like there wasn't a unique solution, so then I just brute-forced it in Excel and came up with the following solutions:

 

1832 x 138 = 252816
1505 x 168 = 252840
1292 x 198 = 255816
1598 x 162 = 258876
1202 x 435 = 522870
1268 x 462 = 585816
4265 x 138 = 588570
4298 x 192 = 825216
4232 x 195 = 825240
7862 x 105 = 825510
4595 x 192 = 882240
1898 x 465 = 882570
4598 x 192 = 882816

Posted by tomarken on 2014-04-15 15:48:32