A real stumper!

Frodo Baggins · 08-11-03, 08:46 PM

Let n be any 5 digit number
Let m = n but with the middle digit chopped off

Find all n for which n/m is an integer

I've been staring at this problem for a bit and I can't figure it out for the life of me.

I think I know how to set it up though:
n is a 5 digit integer. The only way you'll be able to manipulate the center number is to compile the number manually.

Let n = 1000A + 100B + C

Where:

10 <= A <= 100
0 <= B <= 10
0 <= C <= 100

Therefore you are left to prove that:

Code:

               n = km
1000A + 100B + C = k(100A + C)

For any integer k

Where the heck do I go from here? Help me out guys!

Oni · 08-11-03, 09:27 PM

Getting us to do your math homework, eh?

Frodo Baggins · 08-11-03, 10:23 PM

it's not exactly homework (Though it is work and it's done at home)

summer problems I have trouble with

JigPu · 08-11-03, 10:47 PM

I love programming

So, how much will you pay me to write a program to brute-force the answer out?

JigPu

Frodo Baggins · 08-11-03, 10:49 PM

nono, my friend (actually I hate his guts) solved this by hand

besides, even if you may generate the numbers, it's a different thing to generate the general formula for the problem

Frodo Baggins · 08-12-03, 09:41 PM

*hack* *cough*

Oh hello there, did you come to visit my thread?

Shadow ÒÓ · 08-13-03, 06:37 AM

<blows whistle>

Personal Foul!

Unnecessary roughness on the admin!

500 post penalty!

Still second down.

Gawd...the question hurt my brain...I will not even attempt to come up with a forumla now.......but maybe after you can get back in here, someone will have posted an answer for ya. =)

08-11-03, 08:46 PM	Thread Starter #1
Frodo Baggins Member Join Date: Aug 2001 Location: City of Dreaming Spires	A real stumper! Let n be any 5 digit number Let m = n but with the middle digit chopped off Find all n for which n/m is an integer I've been staring at this problem for a bit and I can't figure it out for the life of me. I think I know how to set it up though: n is a 5 digit integer. The only way you'll be able to manipulate the center number is to compile the number manually. Let n = 1000A + 100B + C Where: 10 <= A <= 100 0 <= B <= 10 0 <= C <= 100 Therefore you are left to prove that: Code: n = km 1000A + 100B + C = k(100A + C) For any integer k Where the heck do I go from here? Help me out guys!
	QUOTE Thanks

08-11-03, 09:27 PM	#2
Oni Oni-ni-Kanabō Ninja Hippo eater Moderator Join Date: Apr 2001 Location: St. Catharines, Ontario Canada	Getting us to do your math homework, eh? __________________ Mama, put my guns in the ground. I can't shoot them anymore. On Indefinite Hiatus Asus P6T SE Intel i7 930 @ Stock 12GB Corsair DDR3 9-9-9-24 XFX Radeon 5830 @ Stock Corsair 750 Watt PSU
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08-11-03, 10:23 PM	Thread Starter #3
Frodo Baggins Member Join Date: Aug 2001 Location: City of Dreaming Spires	it's not exactly homework (Though it is work and it's done at home) summer problems I have trouble with
	QUOTE Thanks

08-11-03, 10:47 PM	#4
JigPu Inactive Pokémon Moderator Join Date: Jun 2001 Location: Vancouver, WA	I love programming So, how much will you pay me to write a program to brute-force the answer out? JigPu __________________ .... ASRock Z68 Extreme3 Gen3 .... Intel Core i5 2500 ........................ 4 thread ...... 3300 MHz ......... -0.125 V 2x ASUS GTX 560 Ti ............................... 1 GiB ....... 830 MHz ...... 2004 MHz .... G.SKILL Sniper Low Voltage ............. 8 GiB ..... 1600 MHz ............ 1.25 V .... OCZ Vertex 3 ................................. 120 GB ............. nilfs2 ..... Arch Linux .... Kingwin LZP-550 .............................. 550 W ........ 94% Eff. ....... 80+ Plat .... Nocuta NH-D14 ................................ 20 dB ..... 0.35 C°/W ................ 7 V "In order to combat power supply concerns, Nvidia has declared that G80 will be the first graphics card in the world to run entirely off of the souls of dead babies. This will make running the G80 much cheaper for the average end user." "GeForce 8 Series." Wikipedia, The Free Encyclopedia. 7 Aug 2006, 20:59 UTC. Wikimedia Foundation, Inc. 8 Aug 2006.
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08-11-03, 10:49 PM	Thread Starter #5
Frodo Baggins Member Join Date: Aug 2001 Location: City of Dreaming Spires	nono, my friend (actually I hate his guts) solved this by hand besides, even if you may generate the numbers, it's a different thing to generate the general formula for the problem
	QUOTE Thanks

A real stumper!

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08-12-03, 09:41 PM	Thread Starter #6
Frodo Baggins Member Join Date: Aug 2001 Location: City of Dreaming Spires	hack cough Oh hello there, did you come to visit my thread?
	QUOTE Thanks

08-13-03, 06:37 AM	#7
Shadow ÒÓ Mod in Hiding Join Date: Dec 2000 Location: Pensacola, Florida USA	<blows whistle> Personal Foul! Unnecessary roughness on the admin! 500 post penalty! Still second down. Gawd...the question hurt my brain...I will not even attempt to come up with a forumla now.......but maybe after you can get back in here, someone will have posted an answer for ya. =) __________________ The problem with America is stupidity. I'm not saying there should be a capital punishment for stupidity, but why don't we just take the safety labels off of everything and let the problem solve itself?
	QUOTE Thanks