- I also enjoyed that test (the ACM-12) as a child, but of course that test is for students 4 years older than this test for Tennessee youth (only) is. Also this test is supposed to be limited to the state standards, so should not be the level of the ACM-8 either . But you are right in that they are designed to not allow the dreaded perfect scores (or even tied high values).

-----Original Message-----

From: Jack Brennen [mailto:jfb@...]

Sent: Friday, April 05, 2013 2:30 PM

To: primenumbers@yahoogroups.com

Cc: djbroadhurst; Chris Caldwell

Subject: Re: [PrimeNumbers] Re: Cute dice problem [by induction]

On 4/5/2013 11:20 AM, djbroadhurst wrote:

>

> --- In primenumbers@yahoogroups.com,

> Jack Brennen <jfb@...> wrote:

>

>> Throw the first three dice and figure your sum.

>

> Jack's "first three" seems to be a red herring.

>

Sort of a red herring.

You could replace "throw the first three dice and figure your sum"

with "pick any integer". :)

On 4/5/2013 10:28 AM, Chris Caldwell wrote:

>

> But why would a middle school child recognize that? Surely they did > not want a long calculation. (One of my colleagues said generating > functions give you the answer very quickly--definitely not a middle > school solution!)

Most wouldn't recognize it. I'd like to think I would have recognized it at that age, but I can't be sure. In seventh grade, I scored a 105 out of 150 on the contest that is now called the AMC-12, which was a pretty decent score. If you believe what you read online, Noam Elkies, who is three months younger than me, scored a 112 on that test, and then he proceeded to beat my math competition scores routinely over the next three years.

All of which is to say... a decent math competition should have some problems which are well beyond the capabilities of the average competitor. In ninth grade, I think I was a national co-champion of the Continental Math League competition, because I didn't get a single question wrong all year. It wasn't a particularly satisfying result.

That league was fairly new at the time, and I hope they learned that you need to put some "stretch" questions in with the routine ones. - --- In primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
>

In this little interesting problem, David's "dumb" answer was the dumbness of ordinary arithmetic compared with the elegance of modular arithmetic and induction.

> --- In primenumbers@yahoogroups.com,

> "woodhodgson@" <rupert.weather@> wrote:

>

> > It seems to me there is a very short proof available ....

> > by mathematical induction ....

>

> Indeed:

> http://tech.groups.yahoo.com/group/primenumbers/message/25015

>

> David

>

But, though both give the right answer, I have to "dip the lid" to elegance, even if it requires a bit of effort to bring it about.