Problems

Math Tricks/Problems

21:59:10 Oct 5th 07 - Mr. Sigheart:

I was feeling a bit bored so I decided to make this. Every few days or as long as it takes you to answer the question I'll post another Math trick/problem. I'd like it if you posted how you got to the answer so I know you didn't ask someone else or go on the internet. If it's not answered in 4 days then I'll post how you do it.

First Problem.

Imagine the largest square plug that fits into a circular hole. How well does the plug fit? That is, what percentage of the circular hole does the square plug occupy?

22:42:33 Oct 5th 07 - Mr. Dreadii:

r^2=2phi*r^2

1/2phi = 0.159 = 16%

22:50:27 Oct 5th 07 - Mr. Soccermage:

wrong

23:10:40 Oct 5th 07 - Mr. Asystole:

Ok here's my reasoning.

The square inside the circle will touch at the corners (diagonals). This means the length of the hypotenuse (triange inside the square) will be 1, if we say the circle has radius of 1.

This means the sides of the square are sqrt(2) in length, by pythagorean formula (1^2 + 1^2 = sqrt(2)^2....).

Area of square is 2 square units, length by width. sqrt(2)^2 = 2

Area of circle is pi r ^2, or just pi (as r = 1). 3.14...etc

Area of circle occupied = 2/3.14 = 63.7%

23:22:22 Oct 5th 07 - Mr. Soccermage:

right.

23:25:22 Oct 5th 07 - Mr. Seloc:

next please.

23:28:56 Oct 5th 07 - Mr. Seloc:

While we wait,

Prove that any odd number squared is odd.

00:00:55 Oct 6th 07 - Mr. Acelnorst:

Mr. Seloc

Report

10/5/2007 11:28:56 PM
While we wait,

Prove that any odd number squared is odd.

My math teacher told me when I was 12. therefore it must be.

00:20:40 Oct 6th 07 - Mr. Sigheart:

Good job Asystole, also while I'm at it Dreadii don't be to down that you got that one wrong most people in my class did that immediatly.

All right here's one thats a bit tougher.

a*b=a-b, find [(x*y)*x]*(-y) in simplest form

00:28:21 Oct 6th 07 - Mr. Asystole:

[(x-y)*x]*(-y)
[(x-y)-x]*(-y)
[x-y-x]*(-y)
[-y]*(-y)
[-y]-(-y)
0

don't think this is right but guessing anyhow

00:37:07 Oct 6th 07 - Mr. Asystole:

Any odd number can be represented by 2N+1, where N is an integer

(2N+1)^2

= 4N^2+2N+1

= 4(N^2) + 2N + 1

= X + Y + 1, where X and Y are even (any even times an integer is even)

= Z + 1, where Z is even (any even plus an even is even)

Z + 1 is therefore odd, as any odd plus an even is odd.

00:45:32 Oct 6th 07 - Mr. Sigheart:

Asystole is right.

This one is a hard to show on the computer so I'll do my best.

If a*b=ab-a^2 and atriangleb=a/b-a, then find (2137*2136)/(2137triangle2136)

The triangle means that there is a small triangle between a and b and 2137 and 2136.
The answer is interesting.

00:47:35 Oct 6th 07 - Mr. Gilth:

(x-y)x*(-y)
(x-y)*(-yx)
(x-y)*(x+y)
wrong...(x-y)^2
x^2 - y^2
just messing around

01:23:13 Oct 6th 07 - Mr. Soccermage:

(x-y)^2 does not equal x^2 - y^2

01:26:24 Oct 6th 07 - Mr. Soccermage:

(x-y)^2 does not equal x^2 - y^2

01:58:06 Oct 6th 07 - Duke Tiber Septim IV:

I bet you can't solve my math problem!

2+2=?

Oh yeah...you all are stumped...

02:11:37 Oct 6th 07 - Mr. Sigheart:

Tiber it's 4.

Come on. After this one I'll return to some easier ones.

If a*b=ab-a^2 and atriangleb=a/b-a, then find (2137*2136)/(2137triangle2136)

The triangle means that there is a small triangle between a and b and 2137 and 2136.
The answer is interesting.

03:15:00 Oct 6th 07 - Mr. Asystole:

(2137*2136)/(2137triangle2136)

= [(2137*2136-2137^2)] / [2137/2136-2137]

= [-2137] / [-2135.9995...]

= 1.00047...?

04:31:46 Oct 6th 07 - Mr. Sigheart:

No. But not a bad go, you messed up at a couple points.

05:19:58 Oct 6th 07 - Mr. Asystole:

Unless you're not using typical precedence I don't see it. brackets, exponent, divide/multiply, then add/subtract. Answer would be 1 if a tri b was a/(b-a)

06:22:04 Oct 6th 07 - Duke Tiber Septim IV:

I HAVE ANOTHER!

S+P+A+M=?

06:54:04 Oct 6th 07 - Mr. Dakarius:

Septim
Primarily
Aces
Math?

Doesn't seem right to me, but thats what I came up with.

11:56:15 Oct 6th 07 - Mr. Asystole:

S+P+A+M=Duke Tiber Septim IV

13:04:50 Oct 6th 07 - Mr. Dreadii:

S+P+A+M= Duke Tiber Septim IV / infinity

infinit S+P+A+M= Duke Tiber Septim IV

17:57:07 Oct 6th 07 - Mr. Atreides:

Is the answer 1?

Edit: lol, just realized Asystole said that.

21:17:07 Oct 6th 07 - Mr. Alexander The Great:

what do spam mean , i heard it's meat , but what is it's meaning ??

00:33:48 Oct 7th 07 - Lord Yerean:

uhhhh
ummmm
LOOOOOOOOL
AHAHHAHAHHAHHAAH
EJR:ERG:KSDFDFKL:KSFSDKFJ

Buy C1al!s!!! Free Vi@gr@!!!

----
That's SPAM.
Spam is the term widely used for unsolicited e-mail; spam is also referred to as junk mail. Spam is usually sent indiscriminately to hundreds or even hundreds of thousands of inbox's simultaneous.

02:58:17 Oct 7th 07 - Mr. Sigheart:

I'm horribly embarresed but Atreides and Asystole are both right and I was wrong. I've been checking and rechecking to make sure this next problem is right.

 Andy had an average of 87 on 4 test. What does he have to get on 
  his next test to get an average of 90?

This one's a bit simpler though.

03:16:28 Oct 7th 07 - Mr. Dakarius:

-_- not worth answering.

03:17:29 Oct 7th 07 - Mr. Asystole:

I'll leave the easier ones, someone solve it :)

04:25:20 Oct 7th 07 - Mr. Sigheart:

Expect my next few to be easier as I make sure my harder ones are correct.

06:15:58 Oct 7th 07 - Duke Tiber Septim IV:

Einstein was wrong!

E=MC Hammer

O_o

09:32:24 Oct 7th 07 - Mr. Seloc:

E=MC squared

never agrue with Einstein!

So when this never problem coming?

16:15:36 Oct 7th 07 - Mr. Sigheart:

 Andy had an average of 87 on 4 test. What does he have to get on 
  his next test to get an average of 90?

This one's a bit simpler though.

Here's the next one.

19:04:42 Oct 7th 07 - Mr. Seloc:

*sighs*

19:16:25 Oct 7th 07 - Mr. Spankylicious:

102

19:18:22 Oct 7th 07 - Mr. Sigheart:

Correct

A father in his will left all his money to his children in the following manner:

$1000 to the first born and 1/10 of what then remains, then
$2000 to the second born and 1/10 of what then remains, then
$3000 to the third born and 1/10 of what then remains, and so on.

When this was done each child had the same amount. How many children were there?

19:28:21 Oct 7th 07 - Mr. Spankylicious:

9 children which get $9000 each.

19:56:03 Oct 7th 07 - Mr. Sigheart:

I would have liked an explanation for the problem but your right.

If 4^x + 4^-x = 7, then what is 8^x + 8^-x?

20:20:07 Oct 7th 07 - Mr. Kimms:

Unfortunately, it's Sunday, and i don't do math on Sundays!

20:42:41 Oct 7th 07 - Mr. Spankylicious:

"I would have liked an explanation for the problem but your right."

np...

x - the sum each child gets
y - total sum

x = 1000 + (y-1000)/10 ,but also x= 2000 + (y-2000-x)/10. We now have a system with 2 unknowns, x and y, which can be solved by substitution.

I won't type the entire system because I'm lazy but you get y = 81000 and since we know x = 1000+(y-1000)/10 it means x=9000. We get the number of children by doing x/y = 81000/9000 = 9.

EDIT: and 8^x+8^-x = 47.

21:15:45 Oct 7th 07 - Mr. Atreides:

Cool thread! Unfortunately, as I look through these problems, I get the feeling my HS level math abilities are going to prove insufficient for all but the easiest of these problems =(

21:18:10 Oct 7th 07 - Mr. Spankylicious:

EDIT: I meant y/x not x/y.

"Unfortunately, as I look through these problems, I get the feeling my HS level math abilities are going to prove insufficient for all but the easiest of these problems =("

Are you kidding? The children problem was 8th grade and the 8^x+8^-x is 10th grade.

22:25:25 Oct 7th 07 - Mr. Atreides:

I got the children one....it was amongst "the easiest of these problems."
I probably would have gotten that one too if I remembered any of my math from last year, but in my defense, I just got into 10th grade so I can't be expected to solve 10th grade problems ;)

00:05:31 Oct 8th 07 - Mr. Sigheart:

I just got into 9th grade is my defence and I got the last one.

While I'm at it Spanky you half got it right. I got 18 but this is a sequence and 47 is in the sequence. Just to make sure you got the sequence part tell me the 5 and 6 number in the sequence.

00:14:41 Oct 8th 07 - Mr. Spankylicious:

Sequence? I'm not sure I get what you mean...

17:51:29 Oct 8th 07 - Mr. Sigheart:

Okay they're are a bunch of numbers that this equation could equal. 18, 47, and 7 are part of these numbers. I'd like for you to name the 5 and 6 ones.

The best way to explain it is this. We know y²+y^-2 = 7, and it's obvious that y⁰+y^-0 = 2, so from the recurrence relation (each element is three times the previous/next element minus the element before/after that) it follows that y¹+y^-1 = 3.

Now then continue following these rules and you will see that you will get my answer your answer and a bunch of other answers that make sence.

20:12:57 Oct 8th 07 - Mr. Spankylicious:

Those are 123 and 322.

20:23:17 Oct 8th 07 - Mr. Sigheart:

Okay how about this one.

Find all solutions in nonnegative integers to x⁴ + (x+1)⁴ = y² + (y+1)².

21:22:10 Oct 8th 07 - Lord Yerean:

umm errr ...

i always thought that 2 unknown value equations need 2 equations to be solved...

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