2005 Regional

[Sternhund]

:

How would you do the following?

Number 19: See on test

Number 29: See on test

Number 41: The sum of the digits of the number (2^2000)(5^2005) is: A) 15, B) 13, C) 12, D) 11, E) 10

Number 46: The product of three consecutive multiples of 8 is 30,720. The sum of the three multiples is: A) 72, B) 80, C) 96, D) 104, E) 120

Thanks in advance!

[bradp]

19) I say the area 6 rectangle is 3x2, the area 10 rectangle is 5x2, the area 9 rectangle is 3x3... so the full thing is 8x5 = 40

29) What it turns into is [unparseable or potentially dangerous latex formula]
This helpful formula has shown up on some math tests and NS tests (not recently though)
[unparseable or potentially dangerous latex formula]
I don't know how to derive it.


41) [unparseable or potentially dangerous latex formula]
each [unparseable or potentially dangerous latex formula] turns into a ten, so there are 2000 zeroes with [unparseable or potentially dangerous latex formula] at the front
[unparseable or potentially dangerous latex formula]

46) just try some numbers

[Kurt]

Just an addendum....

For #46, if you call the middle number x:

[unparseable or potentially dangerous latex formula].

The [unparseable or potentially dangerous latex formula] term will dwarf the other one since the RHS is so large...so just take the cube root of the RHS and round up to the nearest multiple of 8 (since the "approximation" will be less than the actual number).

[unparseable or potentially dangerous latex formula]

So [unparseable or potentially dangerous latex formula], and so the sum is [unparseable or potentially dangerous latex formula]

And you can derive the formula for the sum of squares by writing it as a [unparseable or potentially dangerous latex formula] and using summation properties....we did it last year in calculus. :)

You can also use Fermat's Little Theorem to do #41, but it's certainly quicker in this case to do it the way Brad said (but if the numbers weren't so nice, I'd use the theorem).

[stupidityismygam]

sum of squares, use induction!!!!

[bradp]

what if you were on a stranded island and you forgot the formula !?
no induction :(

[stupidityismygam]

Flisendorf :) :) :)

[bradp]

?_?

[stupidityismygam]

ehh, i cant tell you because it was derived by Alex and jmal would yell for giving away our team strategy (lol)...but it is awesome

using it, you get the formula, and then proof it using induction

[bradp]

does your team strategy involve... being dominated by clements ?

[stupidityismygam]

dang it...that was our strategy....dang it...


now we have to devise a new team strategy...GET DOMINATED by KINGWOOD...(lawl)

[bradp]

I wouldn't joke around like that. Kingwood has got some hidden firepower just waiting to dominate next year.

[stupidityismygam]

[bradp]

I have an NS prodigy doing three tests.

per hour.

I got calculator crunchers who spend more time writing the answer than doing the problem.


Just kidding.
It'll probably be just me again next year. Two of kw's science team scores are graduating... and they were also the two math team scores besides me. Some people might step up but i doubt it.

[stupidityismygam]

we have ppl who dont practice at all for uil, but do olympaid problems in their head...


take that

[Kurt]

We have 9th graders...that in the middle of a NS test, stop and talk to each other about World of Warcraft! Take that!

*throws blue pen at annoying 9th graders*

[stupidityismygam]

we have 9th graders who finish the number sense test in 4 minutes, and then go back and draw pictures all over their test (thus get disqualified)

yay for 9th graders

[Kurt]

Well...our 9th graders are finished with their test in about that amount of time too. As in, they aren't willing to do any more. :D

[stupidityismygam]

our fishies laugh at your fishies

[bradp]

at least your freshmen take Ns tests...

[stupidityismygam]

[Kurt]

I bet our freshmen don't even know what USAMO is.

At least I didn't know when I was in 9th grade. :P

...Or 10th, really lol.

Yay for going to a school that doesn't tell people about real problem solving. :)

[NickR]

Heh, at least you guys have freshmen...we only have like maybe two coming up next year and only one this year o.O

And as for USAMO...I'm in the same boat as Kurt...I pretty much found out about that stuff this year : P

[stupidityismygam]

well, to increase your magicalness

you should attempt my olympiad level problems that i am posting in AMC/AIME forums

instead of practicing for something silly like UIL :)

[NickR]

Pssh, who practices for UIL?

And I'll get on that olympiad stuff...but I can't do much of it : P

[stupidityismygam]

well try, it is really hard...

but struggle through it you will benefit :)