Math geekery

[Glenn E.]

I took this test 4 times while in college. As I recall, my best score was about 20, most of which came from getting one of the six problems correct with a lot of supporting work that must have been what they were looking for. I think I also had a 12 and then a couple of 5's or 6's.

http://www.msnbc.msn.com/id/36180644/ns ... eattle_wa/

[Derek T.]

Surely the answer to all six questions is 42?

[Glenn E.]

Yes, but now you have to prove it.

Interestingly, a wrong answer can score more points than a correct answer that lacks sufficient proof. The test is really about showing your work, not getting the right answer. So if you were on the right track but made some minor mathematical error, you could easily score more than someone who got the correct answer but wasn't able to prove it.

[Peter W. Meek]

I did pretty well on the Michigan Mathematics Prize Competition a long time ago (when I was a high-school junior). Enough to get me a partial scholarship. I doubt I could do as well today, though. And I really doubt if I could get anywhere on something like this.

[Glenn E.]

I doubt I could do as well today, though.

I'm reasonably confident that I wouldn't even know where to start on today's questions!

[Derek T.]

Yes, but now you have to prove it.

Interestingly, a wrong answer can score more points than a correct answer that lacks sufficient proof. The test is really about showing your work, not getting the right answer. So if you were on the right track but made some minor mathematical error, you could easily score more than someone who got the correct answer but wasn't able to prove it.

1. 40+2=42
2. 90-48=42
3. 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=42
4. (67x56)-3710=42
5. ((20000000/4000)-3000)-1598=42
6. Fonseca 1963 + Taylor 1927 - Tuke Holdsworth 1922 = 42

Do I get a pass?

[Peter W. Meek]

Like I said not with today's brain

[Peter W. Meek]

I doubt I could do as well today, though.

I'm reasonably confident that I wouldn't even know where to start on today's questions!

I'm not talking about today's questions being harder; I mean today's brain is stupider -- at least in my case. I used to be pretty sharp. Not any more.

As for showing my work; I never could do that. I would look at the problem and see the answer. I never had any idea how I came to it. This caused me terrible problems in school as they always insisted that we show our work. They assumed I was cheating in some way. I finally had to insist on being tested with completely new outside questions while isolated in a randomly chosen room of the school. I looked at the problems and wrote down the answers. I think half the staff still thought I was cheating, but at least I passed math.

Mathematics btw, not arithmetic -- I never could add, subtract, multiply or divide with any skill, or remember the tables. To this day I have to work out things like 6 x 7 = ? by combining things in my head, or by multiplying nearby numbers and plugging them into something like the quadratic equation. Or adding them: 7 + 3 is 10 plus the remaining 3 from the 6 is 13.

To square 98, I square 100 and subtract 2 x 2 x 100 and add 4. ( a^2 + 2ab + b^2 where a is 100 and b is -2). Looking at it another way, consider a 100 x 100 square; take off off a 2 x 100 strip from two adjacent sides, and replace the 2 x 2 square where the strips overlapped and were removed twice.

6 x 7? It's 5^2=25 plus a 5 x 1 strip, a 5 x 2 strip and a 1 x 2 rectangle -- thats 25+5+10+2= 42 ! (How 'bout that?)

Of course it works the other way too: 10 - 4 times 10 - 3 is the 100 square minus a strip of 40 and a strip of 30 with the overlap (4 x 3) added back. 100-40-30+12= 42 again.

I swear: this really is easier for me than remembering the entire multiplication table. Plus, unlike any reasonable multiplication table (my father was made to remember up to 20 x 20 in Canadian schools) this will work for things like 1009 x 1003 -- as long as the numbers are fairly close to an easy-to-square number you can do stuff like this in your head. (BTW, that's a million plus 9000 plus 3000 plus 27 = 1,010,027) (I had this wrong at first, because I mis-remembered what 3 x 9 was.)

[Peter W. Meek]

Hah! I see I "left it to the audience" to actually square 98.

[Glenn E.]

Do I get a pass?

No, you haven't proven that numbers exist.

And yes, I actually had to prove that in a class call Elementary Real Analysis. Elementary, indeed.

I'm not talking about today's questions being harder; I mean today's brain is stupider -- at least in my case. I used to be pretty sharp. Not any more.

Me too... I suspect that today's questions are similar to what I attempted to solve, but I have forgotten all of the finer bits of mathematics in the intervening years. :)

[Glenn E.]

Hah! I see I "left it to the audience" to actually square 98.

My brain works similarly to yours... that's 9800 - 200 + 4. 9604!

[Peter W. Meek]

... forgotten all of the finer bits of mathematics...

Actually, In my case I do mean stupider. Not forgetting details or finer techniques -- serious loss of analytical ability. Two years of 30 drinks (a bottle and a half of 100 proof vodka) a day every day kills a LOT of brain cells. Probably a permanent 30-50 IQ drop. Like I said: I used to be pretty sharp. And, I assume after thirty-odd years, it will never come back.