Solving a problem where letters are assigned numbers

[bambinn]

Hi

So i have a problem were i have 10 letters (C,H,O,L......) and each is assigned a number 0-9 (that i do not know).
5 of these letters + 4 letters gives me = 5 letters
f.x. (not the real problem)
HELLO
+ JOHN
=MELON

I was thinking that if i give the letters numerical value in excel, it would be easier to figure out the answer. H=3, E=2 etc...

Is there a simple way to do this?

[Kaper]

Provided there is a solution (in your sample case - not*) you could try to use Solver for that.

See attachment
- all letters listed in P3:P12 with initial assigned numbers listed in column Q
- words in column B (B2:B4) are spllitted into letters with formula in L2 (I assumed tham max length is 10 letters) with formula (and copy down/left):

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- then letters are converted into digits with formula in L6 (and again copied dowm and left):

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- then "school alike" summing of each decimal position in L10 and possible "in memory" in F11 (and copy left):

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- measure of misfit between row 8 (representation of "sum world") and row 10 (sum of representations of both "added words") in B13 (will be used as goal to be minimized by solver):

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- helper column to check if each digit has been used only once in R3 and copy down:

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Solver settings:
- goal as mentioned above,
- changed cells Q3:Q12,
- constraints for these cells >=0 and <=9 and integer, for R3:R12 =1
- model - evolutionary (available since excel 2010)

*)
1) HELLO
+ JOHN
=MELON
So we know O = 0
HELLO
+ JOHN
=MELON
As O=0, we know L+H = 10 and in next to left column will use +1 from "the rest in memory"
1
HELLO
+ JOHN
=MELON
1+L+0=L so L=L+1 -> impossible!

(I know that you mentioned that it is just an idea - not a real problem, but always it is easier to look for solution once you know there is at least one :-) )

PS. Final idea: one can use brute force method, and try all possible assignments - there is less than 4 millions of possible permutations of 10 letters - shall be possible to calculate in reasonable time.

[Kaper]

PS. It is not alvays easy, and depending on solver settings sometimes it needs few runs of solver
For instance I could find that

kaper
+ smile
= miami

can be obtained with such assignment:
k 2
a 8
p 1
e 4
r 3
s 6
m 9
i 7
l 5
0

after 3 runs.

So probably "bryte force" approach would be a better one.