Comments (5)

1. I think there is a fourth answer.

   327…654…981

   327*2=654 and 327*3=981

   posted by MikeTrig on 6-12-2009 at 8:17 am

2. Looks like you’re correct, MikeTrig; I’ve added yours to the list of solutions.

   One thing I noticed when adding yours is that the top two answers use the same digit-trios in each group… same with the bottom two answers. Interesting!

   posted by Sandy Wood on 6-12-2009 at 8:52 am

3. Sandy, it looks like those two trio are both there because they preserve the order and the digit that moves from the ones digit to the hundreds digit doesn’t carry when multiplied by 3. E.g. 273 -> 327 and 192 -> 219.

   posted by Eric Y. on 6-12-2009 at 11:25 am

4. I notice all the answers sum up to 12…15…18

   Is that some mathmatical rule? Like how the two digits of multiples of 9 add up to 9?

   posted by Michelle on 6-12-2009 at 2:11 pm

5. Yes, Michelle, it is a rule of number theory for both 3 and 9. Any multi-digit number whose digits add up to a multiple of 3 (or 9) is divisible by 3 (or 9). I was taught this as a technique called “casting out 3s”, which can be used for checking math calculations.

   posted by Fred on 6-16-2009 at 5:06 pm

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