Math Games
When the Penguin Group publishing company contacted me to see if I was interested in reviewing Danica McKellar’s popular books, Math Doesn’t Suck, and Kiss My Math, I jumped at the chance. No, it wasn’t for the free books. The time I spend reading and writing doesn’t justify the cost savings. I review products I believe in. Period. For the sake of full disclosure, I received a free copy of each of the two books. That’s it.
Danica McKellar is a well-known actress, a mathematician, and an advocate for Math education. I’m delighted to see people with a tremendous amount of influence use that influence to make Math more accessible.
Richard Berlin, who has been participating in Monday Math Madness! for quite a while, was picked as the winner for this contest by Random.org. Congratulations, Richard! I’ll be sending you your prize so send me your address. Stand by for another Monday Math Madness on Monday at Blinkdagger.
Blinkdagger announced the winner to MMM #14 and now we’re on to MMM #15.
Today’s puzzle comes from Sameer Shah. He submitted it for MMM #13. Even though it’s not the one we picked for that contest, I liked the puzzle and decided to use it for this contest. I’ll be sending Sameer a small gift as a token of my appreciation for presenting me with this nice problem. Here’s Sameer’s problem description, slightly modified:
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Blinkdagger and Wild About Math! are really stirring things up for Monday Math Madness (MMM) contests #13 and 14. And, Texas Instruments is giving away a VERY cool calculator (keep reading for more about the calculator), they’ll ship it internationally, plus we’ll allow anyone to win - even if you’ve won a prize in the MMM contest before. So, we expect submissions from everyone on the planet!
What’s different about the next two contests?
So, what are we doing differently? Well, we’re going to ask you guys and gals to submit your favorite MMM-caliber problems. That’s what you have to do be eligible to win MMM #13. We’ll pick the one we like best and then use it for MMM #14.
- If you submit the problem we pick for MMM #13 then you get one of the awesome calculators.
- If you solve the problem we announce in MMM #14 then you get an awesome calculator.
It seems that Monday Math Madness #12 over at Blinkdagger is tougher than other MMM’s have been. So, there haven’t been many responses to date. So, your chances are higher than in previous contests of winning — if you can solve the problem!
The prize for MMM #11 goes to Chao Xu. Here is Chao’s solution.
A number divisible by 11 if it’s alternating sum of it’s digits is divisible by 11.
We only have 6 numbers, so we have a+b+c-d-e-f divisible by 11, where a to f are variables for each position. The largest possible number formed by a+b+c-d-e-f is 6+5+4-3-2-1 = 9, the smallest number is -9,
Then we have only one number that is divisible by 11 and between 9 and -9 is 0.
We have
a+b+c = d+e+f
a+b+c = (a+b+c+d+e+f)/2
and a+b+c+d+e+f = 21.
a+b+c = 10.5
It’s not a whole number
It shows there is no number can be formed that’s divisible by 11.
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 TeX Embedding failed!10 gift certificate to Amazon.com. For those of you who don’t want a prize I’ll donate $10 to your favorite charity.
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. I’m more likely to post your name if your solution is unique.
We have a winner for MMM #9. It’s Seb Perez-D. Congratulations! Drop me a line to arrange for your prize. And, check out Blinkdagger on Monday for their new problem.
A couple of people were confused about the deadline for submitting a solution. The deadline is 12:01 Tuesday Mountain Time, which is to say Tuesday morning. If you do a Google search for “time California” you’ll know what time it currently is in California. If it’s after 12:01AM the week after a contest is posted then you’re late! Using an offset from GMT will get you into trouble since California changes its offset twice each year.
