IMP 3...POW 7... Crack the Code...HELP QUICK PLEASE!!!

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people have dvised many kinds of secret codes to have private communications with each other, so that no one else can understand their messages.

LETTER SUBSTITUTIONS CODES

Many messages involve words. One of the most popular ways to encode a message of words is to substitute a different letter for each letter of the alphabet.

If the person who gets your message knows your system for replacing letters, it may not be to difficult to figure out your message, because of certain speacial letter combinations or the frequency with which certain letters occur.

A LETTER-NUMBER CODE

This POW concerns codes for arithmetic problems rather that for word messages. To use such a code, you start with an arithmetic problem such as...

35
+ 35
70

To create a coded version of the problem, you replace each number with a letter, always using the same letter for a particular number. For example, you might replace 3 with A,5 with O, and 0 with H. If you so this, the addition problem becomes
AD
+AD
OH

(In using such a code, you need to be careful to distinguish between the number "0" and the letter "0.")

FIGURING OUT THE CODE

It's easy to make up such a code, and it's just as easy to figure out what the coded problem represents if you know the replacement system.

What's more interesting is trying to figure out the code merely by looking at the coded problem written with letters, and you have to figure out what the original arithmetic problem was.

THE RULES

Problems like these usually follow certain rules.

*If a ltter is used more than once in the same problem, it stands for the same number each time it is used.

*Different letters in the same problem always stands for different single-digit numbers.

*A letter standing for 0 never starts with a number more than one digit. For example, the final arithmetic problem can't have a number like "05" (but it can use "507" or "80" or even simply"0").

For some letter problems, it is very easy to reconstruct the original arithmetic problem; for others, it is not tooo hard; and for still others, it is quite difficult. Sometimes there is no possible answer, and sometimes there are many possible answers.

THE PROBLEMS

See whether you can crack the codes for these problems based ont he rules just listed. If you think there is only one right answer, prove it. If you think there are several possibilities, give them all and prove that there are no others. You will need to keep careful track of how you arrive at your answers.

1. A B B
- A
D D

2. S S
+ E E
S S T

3. A B
+ B C
A D E

4. Note: This one is definitely harder than the previous ones.

S E N D
+ M O R E
M O N E Y

5. Make up an example of your own that has a unique solution, and prove that the solution is unique.

I REALLY NEED HELP WITH NUMBER 4 AND 5 ASAP PLEASE
 
Hello, Anoki!

"SEND MORE MONEY" is a classic cryptarithm problem.
. . . I'll get you started on it.


I numbered the columns for reference.

. . \(\displaystyle \begin{array}{ccccc}_1& _2 &_3& _4 & _5 \\ & S & E & N & D \\ + & M & O & R & E \\ \hline M& O& N& E& Y \end{array}\)



\(\displaystyle \text{Adding two four-digit numbers, the maximum sum is 9999 + 9999 = 19998}\)
. . \(\displaystyle \text{In column 1: }\:M = 1\)

. . \(\displaystyle \begin{array}{ccccc}_1& _2 &_3& _4 & _5 \\ & S & E & N & D \\ + & 1 & O & R & E \\ \hline 1& O& N& E& Y \end{array}\)



\(\displaystyle \text{In column 2, }O\text{ must be 0 (zero) and }S = 8\text{ or }9.\)

. . \(\displaystyle \begin{array}{ccccc}_1& _2 &_3& _4 & _5 \\ & S & E & N & D \\ + & 1 & 0 & R & E \\ \hline 1 & 0 & N & E & Y \end{array}\)



\(\displaystyle \text{In column 3: }E + 0 \to N\)

\(\displaystyle \text{Two facts are evident:}\)

. . \(\displaystyle \text{There was a "carry" from column 4. (}N\text{ is one more than }E\text{.)}\)
. . \(\displaystyle \text{And there is no "carry" to column 2: }\:S = 9\)

\(\displaystyle \begin{array}{ccccc}_1& _2 &_3& _4 & _5 \\ & 9 & E & N & D \\ + & 1 & 0 & R & E \\ \hline 1 & 0 & N & E & Y \end{array}\)



\(\displaystyle \text{The next bit of information is well hidden.}\)

\(\displaystyle \text{Recall that N is one more than E.}\)
. . \(\displaystyle \text{In column 4: }\;N + R\:\to\:E\)

\(\displaystyle \text{We have }N\text{, we add }R\text{ (plus a carry, maybe) and get one-less.}\)
\(\displaystyle \text{How does that happen?}\)
. . \(\displaystyle \text{Suppose }N = 7.\)
. . \(\displaystyle \text}Then we see that: }\:\b{7} + 9 \:=\: 1\b{6}\)
\(\displaystyle \text{And }that\text{ is how it happens: by adding a 9.}\)

\(\displaystyle \text{Since 9 is already used, }R = 8\text{, and there was a carry from column 5.}\)

. . \(\displaystyle \begin{array}{ccccc}_1& _2 &_3& _4 & _5 \\ & 9 & E & N & D \\ + & 1 & 0 & 8 & E \\ \hline 1& 0& N& E& Y \end{array}\)


\(\displaystyle \text{The rest takes a bit of trial-and-error . . . I'll let }you\text{ work on it.}\)

 
The story is that a student sent that home as a telegram. Daddy replied with
Code:
SPEND
-LESS
-------
MONEY
It's not as neat as the SEND one. Multiple answers.
-------------------
Gene
 
Hi Tutor

Will you finish (complete) the problem that is currwently posted on your website

SEND
+MORE
__________
MONEY
 
Will you complete cracking the code that was started on your website

SPEND
MORE
+
___________
MONEY
 
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