Comments on: Brain Game: Zero Hour

By: Fred

Fred — Tue, 16 Jun 2009 21:06:00 +0000

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.

By: Michelle

Michelle — Fri, 12 Jun 2009 18:11:00 +0000

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?

By: Eric Y.

Eric Y. — Fri, 12 Jun 2009 15:25:00 +0000

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.

By: Sandy Wood

Sandy Wood — Fri, 12 Jun 2009 12:52:00 +0000

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!

By: MikeTrig

MikeTrig — Fri, 12 Jun 2009 12:17:00 +0000

I think there is a fourth answer.

327…654…981

327*2=654 and 327*3=981