# Wild About Math!Making Math fun and accessible

21Jul/081

MMM #11 is a variation on MMM #9. I promise I won't do any more variations on this problem after this one!

Consider all of the 6-digit numbers that one can construct using each of the digits between 1 and 6 inclusively exactly one time each. 123456 is such a number as is 346125. 112345 is not such a number since 1 is repeated and 6 is not used.

How many of these 6-digit numbers are divisible by 11?

While you may use a computer program to verify your answer, show how to solve the problem without use of a computer.

MMM #9 was interested in divisibility by 8. This contest is interested in divisibility by 11.

I have a Rubik’s Revolution, courtesy of Techno Source, (or \$10 Amazon.com gift certificate) to give to the winner. I’ll give more than one prize if I get lots of correct submissions.

I've changed rule #9 to encourage original solutions, which I'm much more likely to acknowledge:

I may post names and website/blog links for people submitting timely correct well-explained solutions. I'm more likely to post your name if your solution is unique.

Here are the rules for the contest:

2. Only one entry per person.
3. Each person may only win one prize per 12 month period. But, do submit your solutions even if you are not eligible.