Question

Dear Mitch,

First, I just wanted to say how much our daughter and son like their Adler-n-subtract.com Tee shirts! The colors are great, and there's something about the line printed on the back that gets all their friends asking questions...

I gather you give the design credit to a woman in a tee shirt printer local to you, and SHE gives most of the credit to you, saying you knew EXACTLY what you wanted, but whatever it took, they're Perfect!

And now for my question:

Now that Christmas is about to be over, would you happen to have any fun math for New Year's Eve?

My husband and I are going out for dinner, but now that our two children are old enough to stay up until midnight we promised them we'd be home early and celebrate New Year's Eve as a family. And, believe it or not, they actually want to do some kind of math puzzle or something like that (I guess you could say we're a little nerdy that way, but it definitely comes from my husband, as he's the one who was trained as a mechanical engineer before he started his own business.).

Our children are eleven-years-old and thirteen-years-old, and this is the first year we're going to see if they can really stay up until midnight as they're convinced they can.

So any real quick ones that won't frustrate them when they're tired and almost guarantee some kind of success before they fall asleep?

Thank you,

Wishing you another great year of helping spread the message that thinking is fun (and often entertaining!) –

Best of Luck, Health, Happiness during this Holiday Season,

Sandy S.

Plano, TX

Answer

Dear Sandy,

Sure!

Start off by asking them about the current year, which is about to end, 2007.

The question should be this: Is that number, 2007, divisible by any small numbers they can think of?

For example, is it evenly divisible by 2?

Is it evenly divisible by 5?

How about 3?

How about by 9?

(Remind them that by 'evenly' you mean so that there are no remainders, but that their answer could be an odd or even number of times.)

Now, one fun way to present it is to give them this question before you go out and tell them they have to watch the clock and get all their answers completed on a sheet of paper in LESS than five minutes! (no calculators, of course!). And they are to police each other with the clock.

PRETTY HARD TO DO,

UNTIL,

You teach them the little math magic tricks, which you promise to do when you arrive home (a little cliffhanger that ought to at least keep them awake until then!).

And here's how it is done:

There are what's called divisibility tests.

And there is a different but equally miraculous divisibility test for all numbers to be checked for even divisibility by 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.

To answer the questions posed above, you need to know the tests for 2, 3, 5, and 10.

For 2, the big number has to end with a 0, 2, 4, 6, or 8.

2007 does not, so the answer is no, it is not divisible by 2.

For 3, the trick is to add all the digits together of the large number, 2007. So,

2 + 0 + 0 + 7 = 9, and if that sum is divisible by 3 then the whole large number is also. (A small miracle, don't you think?)

So,

Since 9 is divisible by 3, so is 2007.

For 5, the large number has to end with a 5 or a 0.

2007 does not end with a 5 or a 0, so the answer is no, it is not divisible by 5.

For 9, the test is similar to the test for 3.

You add up the large number's digits, 2 + 0 + 0 + 7 = 9, and if that sum, 9, is divisible by 9 then the answer is yes for 2007.

9 is, of course, divisible by 9, so the answer is yes, 2007 *is* divisible by 9.

Finally, for 10, the large number has to end with a zero.

2007 does not, so the answer is no, it is not divisible by 10.

Now, when you and your husband arrive home, in whatever time is remaining before the clock strikes 11:30, if possible, to give the family a half hour afterwards to prepare to celebrate the new year coming in, as a family try these same math questions on 2008. Then try 2009, and especially 2010, which should yield a lot of positive answers!

Hope this helps.

Happy New Year!

-- Mitch