Part $2$: SEND MORE MONEY! $[60$ marks$]$

You recelved the following cryptic message $($which you have identified that it is not a scam$)$ from your secret

agent partner, requesting you to send over some amount indicated by the following sum:

SEND$+$MORE$=$MONEY

Here, it is understood that each letter represents a unique digit $(0$ to $9)$ and no two letters share the same

digit.

For instance, consider the following mapping:

Using this mapping, SEND represents $9567,$ MORE represents $1085,$ and MONEY represents $10652.$ This is

correct because $9567+1085=10652.$

In this task, your final goal is to determine what digit each letter represents, and hence the amount of

MONEY that your partner is requesting. To help you out with this problem, it will be split into various parts,

and you will get to consolidate these into a functional algorithm at the end. Part $2$A: Does it work? $[15$ marks$]$

First, we will try to find if a given mapping is valid. There are $2$ criteria that determines if a mapping is valid.

The first digit of a word cannot be $0$

The addition result must be correct

Write a function check$($puzzle$,$ mapping$)$ that takes in the puzzle as a tuple and the mapping as a dictionary

and returns the dictionary if it is a valid mapping, and False otherwise

Input:

puzzle $($of type tuple$).$ Contains a tuple of at least $2$ elements. For a $n-$sized tuple, the first $(n-1)$

elements are words that are to be added together, and the $n-$th element is the result that it should

add up to

mapping $($of type dictionary$).$ Contains a dictionary where the key is the alphabet, and the value is

the corresponding integer.

Output:

If it is valid, return the dictionary $($i$.$e$.,$ the mapping$)$

CS$1010$E Assignment $3$

AY$2022/2023,$ Special Term $2$

Else, return False Part $2$B: Unique Letters $[10$ marks$]$

Now, let us try to tackle the puzzle. We will first need to find out what are the alphabets that are present

within the puzzle.

Write a function unique$\_$letters$($puzzle$)$ that takes in the puzzle as a tuple and returns a tuple of letters

present within the puzzle. The output should not contain any duplicated alphabets.

Input:

puzzle $($of type tuple$).$ Contains a tuple of at least $2$ elements. For a $n-$sized tuple, the first $(n-1)$

elements are words that are to be added together, and the $n-$th element is the result that it should

add up to

Output:

A tuple of the unique elements within the puzzle. The ordering of the output does not matter

Examples:$(\text{'}$D$\text{'},\text{'}$Y$\text{'},\text{'}$S$\text{'},\text{'}$N$\text{'},\text{'}$R$\text{'},\text{'}$E$\text{'},\text{'}$M$\text{'},\text{'}$O$\text{'})$ Part $2$C: Exploring the possibilities $[25$ marks$]$

Let us try to find a possible mapping for the puzzle. This may seem hard, but we will try to guide you

through the thought process so don't worry!

Given a sequence of alphabets within the puzzle and a sequence of numbers which we could match the

alphabets to$,$ write a function assign$($letters$,$ numbers$\_$left, mapping, puzzle$)$ that will determine a

possible mapping that satisfies the puzzle, if it exists.

To better illustrate what each parameter is$,$ below are a few examples explained:

Example $1$:

This means that for the puzzle $A+B=C,$ which I have decided that $A=2,$ I still need to assign some

numbers to $"$ B $"$ and $"$C$"$ to satisfy the puzzle, where they could either take up the values $5,6$ or $8$

In this case, the algorithm will determine correctly that B can be $6,C$ can be $8$ and hence return $\{\begin{array}{c}{?}^{\text{'}\text{'}}{A}^{\text{'}\text{'}}\text{:}2\end{array},$

$"$B$"$:$6,"$C$"$: $8\}$

Example $2$:

This means that for the puzzle $A+B=C,$ which I have decided that $A=1,1$ still need to allocate $"$B$"$ and

$"$ C $",$ where they could either take up the values $2,4,6$ or $8$

In this case, there is no possible way of doing it$,$ and hence the algorithm will return False

Input:

letters $($tuple of characters$)-$ the letters that have yet to be allocated a mapping

numbers left $($tuple of integers$)-$ the numbers that can be mapped to the lettersPart $2$D: Putting it together $[10$ marks$]$

Nice! Now that we have all the functions required, we can solve the cryptic message we received.

Given the $3$ functions defined earlier, write a function solve$($puzzle$)$ that returns the corresponding

mapping. If the puzzle is not solvable, return False

Input:

puzzle $($tuple$)-$ the addition puzzle as described in earlier parts

Output:

If the puzzle is solvable, return the final mapping

If it is not solvable, return False

Examples: