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Vaneet Dadra

Guest

Two +three +seven =twelve

TWO
+ THREE
+ SEVEN
      ------
   TWELVE   

Can someone help me in answering above puzzle:( please....;)

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: Two +three +seven =twelve

huh?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Two +three +seven =twelve

You need to replace each letter with a digit to make the sum work. So for example, T has to be 1 because TWELVE is 6 digits but everything else is only 5 or less, so it won't add to more than 199999.

W has to be 0, because once you've filled the T in THREE in as a 1, the total can't be more than 119999. 1 has been taken already, so 0 is the only possibility.

Using that kind of reasoning should hopefully be able to fill in the rest of the puzzle too. This is as far as I've got so far though.

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Why did the vector cross the road?
It wanted to be normal.

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: Two +three +seven =twelve

Sorry my bad Vaneet. I thought you had trouble in how 2 + 3 + 7 = 12 so I was like HUH? lol

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Two +three +seven =twelve

The question comes from here: http://www.mathsisfun.com/twelve.html

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Pathik

Guest

Re: Two +three +seven =twelve

Go figure..
BTW I know why you want it.

Vaneet Dadra

Guest

Re: Two +three +seven =twelve

I figured it out Pathik....

Vaneet Dadra

Guest

Re: Two +three +seven =twelve

Any other advice.,;)

Dragonshade

Member

Registered: 2008-01-16

Posts: 147

Re: Two +three +seven =twelve

I made these equations according to table

O+E+N=10y +E  ( y=1 or 2)
y+W+2E=10x+V (x=0,1,2)
x+T+R+V=10z+L (z=0,1 or 2)
z+H+E=10a+E (a=1 or 2)
a+T+S=10T+W

E 6 times
T 3 times
V 2 times
W 2 times
R 1 time
H 1 time
N 1 time
O 1 time

These letter represent 8 diff number out of 10

lets take all number to the max 999+99999+99999= 200997
T could only be 1 or 2 ,   
If we assume T = 2
a+T+S=10T+W
T+S <=18
a must be 2 , then 2+T+S <20, which contradicts
so T must be 1

Last edited by Dragonshade (2008-05-16 16:20:53)

Dragonshade

Member

Registered: 2008-01-16

Posts: 147

Re: Two +three +seven =twelve

Simplifying the equations

O+N=10y  ( y=1 or 2)
y+W+2E=10x+V (x=0,1,2)
x+1+R+V=10z+L (z=0,1 or 2)
z+H=10a (a=1 or 2)
a+S=9+W

O+N=10y (y=1 or 2)
since they both smaller than 10 , y could only be 1

O+N=10
y+W+2E=10x+V (x=0,1,2) = 1+W+2E=10x+V (x=0,1,2)

z+H=10a (a=1 or 2)
and z could only be (0,1 or 2)
H< 10, z can't be zero  , so z could only be (1, or 2)
a could only be 1

a+S=9+W
1+S=9+W
S-W=8
W might be 0 or 1, S might be 8 or 9

According to Mathsyperson, W could only be 0
then S could only be 8

Simplify the equations again

O+N=10
1+2E=10x+V (x=0,1,2)
x+1+R+V=10z+L (z=1 or 2)
z+H=10
W=0
S=8
T=1

H is different from S , then z=1 , H = 9

x+1+R+V=10z+L

we know that W=0 T=1, S=8, H=9
This is the only equations left:
O+N=10
x+R+V=9+L (x=0,1,2)
1+2E=10x+V

Eliminate the x
2E+10R+9V=89+10L
V must be odd , options are 3,5,7
the only even numbers left : 2,4,6

O+N=10, so O,N could either take (3,7)(7,3) or (6,4) (4,6)
Since O and N only appear once, so order doesnt not matter

Consider O , N take (7,3)
V has to be 5
2E+10R=44+10L
E+5R=22+5L
E+5(R-L)=22
E,R,L have to be any arrangement of (2,4,6)
No solution

Thus, O,N have to take (6,4)
2E+10R+9V=89+10L
E+5(R-L)= (89-9V)/2
V = 3, 5, 7
E+5(R-L)=31   (2,5,7)
E+5(R-L)=22   (2,3,7)
E+5(R-L)=13     (2,3,5)

When V=5 E=2, R=7, L=3 , equation two has solution , 2+5x4=22

So
TWO = 107  THREE= 19722 SEVEN=82523   
Or
TWO=103 THREE=19722 SEVEN=82527

Fixed!!!

Last edited by Dragonshade (2008-05-17 07:52:08)

Dragonshade

Member

Registered: 2008-01-16

Posts: 147

Re: Two +three +seven =twelve

     TWO                106               104
   THREE              19722             19722
   SEVEN        =     82524     or  =   82526
-----------       ------------      ------------
  TWELVE             102352            102352

Last edited by Dragonshade (2008-05-18 07:47:03)

LizD

Guest

Re: Two +three +seven =twelve

Can't be right as there is no 4 used - I thought e.g. E had to keep its value in each line of the equation...

Dragonshade

Member

Registered: 2008-01-16

Posts: 147

Re: Two +three +seven =twelve

Can't be right as there is no 4 used - I thought e.g. E had to keep its value in each line of the equation...

It was my mistke， N,O take the value of 6,4 , I put it wrong, , just a minor mistake

LizD

Guest

Re: Two +three +seven =twelve

Great - now I can give it to the kids at school - you're a star!

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Two +three +seven =twelve

Dragonshade: I put your solution on the main website here: Solution - TWO + THREE + SEVEN = TWELVE

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman