Brain Teaser

K

Kaycee

New member
Joined
Aug 26, 2005
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24
For each of the following, replace the letters with digits in such a way that the computation is correct. Each letter may represent only on digit.

Lyndon
X B
Johnson
__________

MA

MA
+
MA
_______
EEL

I got for Letter
M= 7
A=6
E=2
L=8
I dont know how to get the numbers for Lyndon and Johnson or Letter B
Unless B = 0
Can anyone help me out Please
Thank You
 
If 1 to 9 allowed (no zero), then B = 9 and ON = 75. Good luck!
 
So would you take 9 and times it by Lynd75 and get 2765465 and then take 9 times Johns75 and get 18765475 then would you add those numbers togethet or how would you do it.
Please help
Thank you
 
Hello, Kaycee!

I don't understand what you're trying to do . . .

So would you take 9 and times it by Lynd75 and get 2765465 . . . how?
and then take 9 times Johns75 and get 18765475 . . . how?
then would you add those numbers together or how would you do it. . . . add?
Click to expand...
Code: 
     L Y N D O N
     x         B       It is a straight-forward multiplication,
   --------------             (but NOT an easy problem).
   J O H N S O N
We can see that B ≠ 0, L ≠, and J ≠ 0.

Also: B ≠ 1 . . . otherwise: LYNDON x 1 = LYNDON


This could take quite a while . . .

If we conjecture that B = 9, we have three cases to investigate:
Code: 
     L Y 5 D 2 5         L Y 5 D 7 5         L Y 0 D 5 0
   x           9       x           9       x           9
   -------------       -------------       -------------
   J 2 H 5 S 2 5       J 7 H 5 S 7 5       J 5 H 0 S 5 0
I'll wait in the car . . .
 
In the math problem I have is
Lyndon
Times B
Times Johnson
The equal sign does not come till after johnson
Like you have Ly5d25 time 9 equals Johnson
this is not how my math problem is.
It is like the way I typed it at the beginning of this page
Please help
 
L Y 5 6 2 5
x 9
-------------
J 2 H 5 6 2 5

Doesn't work, because

9 * 5 = 45
9 * 2 = 18, 18 + 4 = 22

The only thing that gives 5 in tenth when multiplied by 9 is 6, so D = 6:

9 * 6 = 54, 54 + 2 = 56, S = 6

D cannot be equal to 6, therefore this doesn't work.
 
..LYNDON
.........x.B
JOHNSON

.....__-__-__-__-__-__
...........................__
__-__-__-__-__-__-__

1--If B = 2....3....4....5..........6.........7....8....9
.......N can be..0...0,5...0..0,5.....0,2,4,8...0,5...0...0,5
2--If N = 0, then there is no carryover from BxD
3--Then, DONxB = SON stands alone.
4--If N = 0, then O cannot = 0.
5--If B = 3, 5, 7, or 9, O must = 5
6--Then
N......B......D......S
0.......3......1......4....Okay
0.......3......2......7....Okay
0.......5..NG as O = 5
0.......7......-.......-.....NG
0.......9......-.......-.....NG
7--Two possible results
(1)..150...(2)..250
.......x.3.........x.3
......450.........750
8--Then, LYx3 = J5H
9--J = 2 max. = 2 as D = 1
10--In (1) 6, 7, 8, and 9 are available for L,Y,J, and H.
11--If Y = 6, H = 8 but L must be 8 also - NG
.....If Y = 7, H = 1 but D = 1 - NG
.....If Y = 8, H = 4 but S = 4 - NG
.....If Y = 9, H = 7, 3L + 2 cannot = 25 - NG
12--In (2) 1, 4, 6, 8, and 9 aew available for L, Y, J, and H.
13--If Y = 1, N = 3 - NG
.....If Y = 4, H = 2 - NG
.....If Y = 6, H = 8 but L must = 8 to make 3L + 2 = 25 - NG
.....If Y = 8, H = 4 and 3L + 2 cannot = 25 - NG
.....If Y = 9, H = 7 and 3L + 2 cannot = 25.
14--Therefore, B is not 3, 5, 7, or 9 and must be 6.
15--N can therefore be 0, 2, 4, 6, or 8
16--Then, for B = 6
N......O......D......S
0.......2.......1......7
0.......4.......1......8
0.......8.......-.......-
2.......-........-.......-
4.......-........-.......-
8.......-........-.......-
17--Two candiates fall out (1)..120.and (2)..140
............................................x.6.............x..6
...........................................720.............840
18--In (1) 3, 4, 5, 8, and 9 are available.
19--J can be a max. of 5 and = 3, 4, or 5
20--This path leads to no solutions.
21--In (2) 2, 3, 5, 7, and 9 are available
22--J can be a max. of 5 and = 2, 3, or 5.
23--J = 2 and 5 lead nowhere.
24--For J = 3, we have LY
................................x..6
...............................34H
25--340/6 = 56.6666 so LY must be 57 or greater.
For LY = 57, 57x6 = 342 What do you know. Home free.

So we have 570140
..........................x..6
...................3420840
 
what? didn't understand anything... haven't ever solved such problems. maybe you can gimme some links to simpler ones? :p
 
Dark Knight 496 said:
what? didn't understand anything... haven't ever solved such problems. maybe you can gimme some links to simpler ones? :p
Click to expand...

Those are known as "alphametics", DK; do a google search.
Seems that Kaycee doesn't know what they are...
There are 9 different letters in "lyndon b johnson"; normally,
digits 1 to 9 would be used, but that's not always the case;
in this case 0 is used (not 9) as TchrWill showed; and I can
confirm that his solution is the ONLY one.

Kaycee, YOU should also do a google search on alphametics...
you'll see what I mean...
 
I can't find anything in google on how to solve alphametics... I could only find more examples. I can figure out some digits by seeing how many can be carried over and other stuff, but that only lets me know a few of the digits. Then for the rest, there are no signs of what they are supposed to be... :(
 
I think I got the numbers but not sure
L 3
Y 1
N 5
D 4
O 7
N 5

B 2

J 1
O 7
H 8
N 5
S 3
O 7
N 5
Please let me know if this is Right Please
Thank you
 
You've been provided with the fully-worked solution, one that complies with the requirements of the problem. Why not just use that one?

Eliz.
 
You have to be wrong about the equal sign being after JOHNSON. Otherwise ANY numbers you put in would work (except L & J can't be 0) 'cause you don't know the result of any computation. It must be
LYNDON times B = JOHNSON
 
Dark Knight 496 said:
I can't find anything in google on how to solve alphametics.
Click to expand...
As was demonstrated very completely by "TchrWill", the process involves methodically testing the various options. There is no "formula" but time and hard work.

Eliz.
 
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