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12-05-2012 02:59 AM  7 years ago
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red_z06

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Dumont, NJ

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Let see how smart some of you guys are.
Find this 3 digit number that satisfies following condition.

1. 10th place number is 6

2. Switching 100th and 1th number causes the new number to be smaller than the original by 297.

3. Switching 100th and 1th of the original number and adding 179 to it will turn the new number to have same 100th 10th and 1th digits. For example 111, 222 etc.
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12-05-2012 03:22 AM  7 years ago
utahbob

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St. George Utah

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💎Sustaining Member
huh?
aah--aah--aah--90210?
I do a great decending funnel!
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12-05-2012 04:40 AM  7 years ago
baldgeek

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New Zealand

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562
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12-05-2012 04:48 AM  7 years ago
PsychoZ

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Northern, CA

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42, it is the answer to everything including life itself.Tea Parties are for little girls with imaginary friends
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12-05-2012 11:20 AM  7 years ago
JoseA

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South Chicago

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8765309

I'll email my pay pal info...
The ignored one
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12-05-2012 11:27 AM  7 years ago
red_z06

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Dumont, NJ

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Ding Ding Ding. We have a correct answer.

Very nice Baldgeek.
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12-05-2012 03:56 PM  7 years ago
PsychoZ

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Northern, CA

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8765309
Actually it was 8675309, but close.

http://en.wikipedia.org/wiki/867-5309/Jenny
Tea Parties are for little girls with imaginary friends
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12-05-2012 04:02 PM  7 years ago
titillater

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Duncan B.C

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How is that a 3 digit number?
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12-06-2012 12:33 PM  7 years ago
Climax

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West London, United Kingdom

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That's a fun problem!

I'm not sure if this is the best way to solve it, but this is what I did... If there is a better method, then please post!

Let the answer be N, and in terms of digits this would be represented as X6Y - So all we need to do is find X and Y...

So from point (1) you can form the following equation,

N = 100X + 60 + Y

Now taking point (2) into account you get,

100Y + 60 + X + 297 = N
100Y + 60 + X +297 = 100X + 60 + Y

Which simplifies to,

X - Y = 3 (Remember this as equation 1)

OK, you just need one more equation relating X to Y and you can then solve them as a simultaneous pair

From point (3)

100Y + 60 + X + 179 = 100Z +10Z + Z

Where Z represents the digits in either 111 to 999 (i.e. ZZZ, as described in point 3 of the problem)

This simplifies to,

100Y + 60 + X + 179 = 111Z (Remember this as equation 2)

You still need to figure out Z, here's what I did...

We know that in the answer the middle digit is "6" (as we have been told this in the question)

We also know (in symbolic terms) that Y6X + 179 = ZZZ

Now consider the middle digits, here 6 + 7 = 13. So it would appear that the middle Z might be a "3" with a carry that ripples up (13 = 10 + 3, or 3 carry 1). It also possible that there was a "carry up" from the lower down X + 9 component, in which case the middle Z would be a 4.

So we now know that Z is either 3 or 4. Now if you think about it, it can't be a "3" as there is always a carry from the lowest digit. Why, well if Z is 3 or 4, then the X + 9 component will always generate a carry!

So Z = 4

This means that equation 2 becomes,

100Y + 60 + X + 179 = 444

Which simplifies to,

100Y + X = 205 (Remember this as equation 3)

We now have 2 equations in X and Y

100Y + X = 205
X - Y = 3 (this was equation 1 from above)

Let's find X...

X = 3 + Y

Then substitute in to equation 3,

100Y + (3 + Y) = 205
101Y = 202
Y = 2

Then as X = 3 + Y,

X = 5

Which means that the answer is 562

I'm sure there must be a simpler way, any ideas?
Electronics, Physics, Helicopters, Fixing Things...
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12-06-2012 02:00 PM  7 years ago
Shawn Pierce

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Yeah, i did 3rd one first. 222-179=43 333-179=154 444-179=165 555-179=376 666-179=487 777-179=598 888-179=709 999-179=820

444 is the only one with a 6 in middle. reverse numbers and double check 562-265=297
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12-06-2012 02:07 PM  7 years ago
Climax

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West London, United Kingdom

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I guess what I was trying to do was to formulate a couple of simultaneous equations to solve the problem without have to do it heuristically at any stage. i.e. avoiding the "try out the possibilities" approach that's made easy by step 3...

Which I couldn't really do!
Electronics, Physics, Helicopters, Fixing Things...
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12-06-2012 02:49 PM  7 years ago
mr dan

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Stockton Calif

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Wow Im very impressed (Yawn!)
But can you you fly inverted while holding your TX behind your back, hanging upside down and drinking a soda?
"R.I.P Roman" Citizen 0094 in the Nation
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12-06-2012 04:48 PM  7 years ago
red_z06

rrProfessor

Dumont, NJ

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I started it the way Climax did. But, forgot that

N = 100Y + 60 + X + 297

LOL

So I ended up with 2 eq and 3 unknowns. Someone solved it in a simpler fashion.

BTW, the original (Korean) problem stated this was from a 2nd grade math problem. It is hard to believe. But, considering that, perhaps they were seeking the methond Shawn was using. I hated to do the plug in method but in this case it only took 9 tries.

Nice one Shawn.
www.JustinJee.com
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12-06-2012 05:11 PM  7 years ago
red_z06

rrProfessor

Dumont, NJ

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This is how one guy solved it.

A = 100th digit
B = 1th digit

B6A+179=CCC

Since A is 100th digit, it can't be zero.
If A can't be zero, then C=4 (for the values of A 1 through 9)

So, 444-179=265

B=2
A=5

Answer is 562.
www.JustinJee.com
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