Math Riddle

[Dayz V@mp!re]

Ok so you start out with a 4 digit number

1234

then move the numbers down till you get the first number in the last spot

1234
4123
3412
2341

then add all the numbers up

1234
4123
3412
2341
--------
11110

then you add your first numbers

1+2+3+4=10

then you divide

10/11110=1111

you can do this with any 4 digit number and it will equal 1111 why does it do that?

[Troll King]

1111 is the sum of the exponents of 10 from 1 to 1000 (as in 1 + 10 + 100 + 1000).

When you take a four digit number, you
can express it in place holders as in:

1234 = 1 * 1000 + 2 * 100 + 3 * 10 + 4 * 1

When you shifted the numbers around you got:

4123 = 4 * 1000 + 3 * 100 + 2 * 10 + 1 * 1

and so forth.

When you added the four combinations together, and rearrange the figures again into exponents of 10, you get:

1 * 1000 + 2 * 1000 + 3 * 1000 + 4 * 1000 + 1 * 100 + 2 * 100 + 3 * 100 + 4 * 100 + 1 * 10 + 2 * 10 + 3 * 10 + 4 * 10 + 1 * 1 + 2 * 1 + 3 * 1 + 4 * 1

Factoring that expression, you get:

1000 * (1 + 2 + 3 + 4) + 100 * (1 + 2 + 3 + 4) + 10 * (1 + 2 + 3 + 4) + 1 * (1 + 2 + 3 + 4)

Again you can factor out the (1 + 2 + 3 + 4) and you will get:

(1 + 2 + 3 + 4) * (1000 + 100 + 10 + 1)

or

(1 + 2 + 3 + 4) * (1111)


I left the bracketed part as (1 + 2 + 3 + 4) to illustrate that it doesn't matter what four digits comprise the original number, as you will still get an expression of the sum of those digits multiplied by 1111.


Of course, one should note that any 4 digit numbers that contain a zero will still work as long as you keep the zero as a placeholder throughout:

i.e. 1000 -----------> 1000 + 0100 + 0010 + 0001

[Dayz V@mp!re]

Thanks its extra credit in my math class

[stark]

and the teacher does the homework.

[syzygy]

Originally posted by Dayz V@mp!re
Thanks its extra credit in my math class

plz tell me that's an algebra test.

[Epinephrine]

Originally posted by syzygy
plz tell me that's an algebra test.

Syzygy where did you get your name from? I ask because some friends of mine in High School made a 3D shooter called that and I thought they had randomly made that name up.

-Epi

[Sleepy Weasel]

syz·y·gy ( P ) Pronunciation Key (sz-j)
n. pl. syz·y·gies
Astronomy.
Either of two points in the orbit of a celestial body where the body is in opposition to or in conjunction with the sun.
Either of two points in the orbit of the moon when the moon lies in a straight line with the sun and Earth.
The configuration of the sun, the moon, and Earth lying in a straight line.
The combining of two feet into a single metrical unit in classical prosody.



Also the only word with 3 y's in it.

[Arc]

lol

[pete_w]

[syzygy]

Originally posted by Epinephrine
Syzygy where did you get your name from? I ask because some friends of mine in High School made a 3D shooter called that and I thought they had randomly made that name up.

-Epi

as weasel stated, it's a word, the only english word with 3 y's, and also the only english word with "yzy" in it. but i first heard it in the archives of Atari. turns out it was the first chosen name for the company, but a shoemaker had the name taken. nowadays, search on google and u get tons of references and companies using syzygy.

[Mr. Peanuts]

he nicked it from a UT 2003 bot name

[MaGi kOz]

A little boy was asked the question:

What is the sum of all of the numbers from 1-100? (as in 1+2+3+etc+100)

The kid thought for a few seconds then replied with, "That's easy! The answer is 5050!"

How did he come up with the answer so quick?

[Epinephrine]

101 * 50 = 5050

aka (1+100) + (2+99) + (3+98) + ... + (50+51)

And that little boy's name was... Gauss.

Originally posted by MaGi kOz
A little boy was asked the question:

What is the sum of all of the numbers from 1-100? (as in 1+2+3+etc+100)

The kid thought for a few seconds then replied with, "That's easy! The answer is 5050!"

How did he come up with the answer so quick?

[MaGi kOz]

Originally posted by Epinephrine
101 * 50 = 5050

aka (1+100) + (2+99) + (3+98) + ... + (50+51)

And that little boy's name was... Gauss.

i was thinking:

(1+99) + (2+98) + ... + (49+51) + (50) + (100)

I guess that's the same thing.