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Step by Step Solution to Crypto-Arithmetic ProblemCrypt-Arithmetic Problems are substitution problems where digits representing a mathematical operation
are replaced by unique digits.
Like : P L A Y S + W E L L = B E T T E R
Where each unique alphabet represents a unique digit from among 0 to 9. So, if the solution to this puzzleis to be found, it would be (after a long computation) : 9 7 4 2 6 + 8 0 7 7 = 1 0 5 5 0 3
The basic rules are :
Each unique digit must be replaced by a unique character.
The number so formed cannot start with a ZERO.
There is no efficient way to calculating the correct substitution except simple mathematical deductions
utilizing additive identity (which is a really cryptic way of saying A + 0 = A), multiplicative identity (A * 1 =
A), and hit-and trial.
The solution becomes unmanageable if a systematic approach is not followed. So, here's a step-by-step
approach to solving a Crypt-Arithmetic Problem.
C1 C2 C3
S E N D
M O R E
+______________
M O N E Y
SOLUTION
Value ofM = 1 [ S
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7/28/2019 Step by Step Solution to Crypto.docx
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Now, analyzing and deducing values from Right to Left, we get
If C1 = 1, S = 9 Then C1 + S + M = 11, which makes O=1 [False].
if C1 = 1, S = 8, Then C1 + S + M = 10, which makes O = 0.
if C1 = 0, S = 9, then C1 + S + M = 10, which makes O = 0.
So, O = 0 is valid.
Now, Both the above given alternatives look equally probable at the moment.
Since O = 0, E + O + C2 will give carry only when C2 = 1 and E = 9.
But, that will give E + O + C2 = 10, and N=0. [False, O = 0 is already established]
So, the second alternative must be correct, i.e. C1=0, S=9, O=0, M=1.
Now, E + O + C2 = E + C2 = N.
If C2 = 0, then E = N [Invalid]
so, C2 = 1 and N = E + 1
Also,
N + R + C3 = E + 10
E + 1 + R + C3 = E + 10
or, R + C3 = 9
Now if C3 = 0, R = 9 [Invalid, S = 9]
So, C3 = 1 and R = 8.
Now,
Choices For E = {2, 3, 4, 5, 6, 7 } so N = {3, 4, 5, 6, 7, 8 }
But 8 is already taken.
So, E = {2, 3, 4, 5, 6} and N = {3, 4, 5, 6, 7}
Now,
D + E = 10 + Y >= 12
so, (D,E) = { (5, 7), (6, 7), (7, 5), (7, 6) } which means N = { 6, 7, 8}But 8 is already taken so N = {6, 7}
so, (D, E) = { (7, 5), (7, 6)} i.e D = {7} and E = {5, 6}
Now, if E = 6, N=7 [invalid, 7 is already taken, D = 7]
so , E = 5, N = 6 and Y = 2.
Hence the Solution becomes ,
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7/28/2019 Step by Step Solution to Crypto.docx
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S = 9, E = 5, N = 6, D = 7, M = 1, O = 0, R = 8, Y = 2.
i.e. 9 5 6 7
+ 1 0 8 5
________
1 0 6 5 2
That's about it.
There is an online tool to calculate the solution to these problems. Its onhttp://bach.istc.kobe-u.ac.jp/cgi-
bin/crypt/crypt.cgi?crypt=plays+well+better.
Thank You.
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