Last Friday Blinkdagger announced a winner for MMM #8. Here's MMM #9:
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 8?
While you may use a computer program to verify your answer, show how to solve the problem without use of a computer.
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.
Here are the rules for the contest:
1. Email your answers with solutions to mondaymathmadness at gmail dot com.
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.
3. Your answer must be explained. You must show your work! Wild About Math! and Blinkdagger will be the final judges on whether an answer was properly explained or not.
4. The deadline to submit answers is Tuesday, July 1, 2008 12:01AM, Pacific Time. (That’s Tuesday morning, not Tuesday night.)
5. The winner will be chosen randomly from all timely well-explained and correct submissions, using a random number generator.
6. The winner will be announced Friday, July 4, 2008.
7. The winner (or winners) will receive a Rubik's Revolution or a $10 gift certificate to Amazon.com.
8. Comments for this post should only be used to clarify the problem. Please do not discuss ANY potential solutions.
9. I may post names and website/blog links for people submitting timely correct well-explained solutions.