# How to solve a cryptarithm?

Given multiplication is $$\begin{array}{cccccc} & & & P & E & N \\ & & & I & N & K \\\hline & & L & K & P & R \\ & I & R & T & N & \\ E & A & K & N & & \\\hline L & E & T & T & E & R \end{array}$$

how to find the values of the letters?

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If you get stuck: math.ubc.ca/~israel/applet/metic/metic.html – user641 Apr 20 '11 at 23:37

Start from N*N ends in N, so N must be 5 or 6 (can't be 0 or 1 from the second line in the sum). Then I*N ends in N (and I !=1) says N is 5 and I is odd. Then K is even and R is 0. Continue

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@Whoever it was that posted a comment: your math didn't render, and was breaking the comment display, so I removed it. Please try to re-post it correctly. – Willie Wong Apr 20 '11 at 21:04
Can we be sure that the second block represents: $\begin{array}{llllll} &&K &(P & E & N) \\ &N &(P & E & N)& \\ I &(P & E & N)&& \\ \end{array}$ and not: $\begin{array}{llllll} &&N &(I & N & K) \\ &E &(I & N & K)& \\ P &(I & N & K)&& \\ \end{array}$ – Hank Apr 20 '11 at 21:36
It has in all cryptarithms I have ever solved and matches the way I was taught to do multiplication. – Ross Millikan Apr 20 '11 at 22:28

## 6 1 5 * 354

 2 4 6 0


3 0 7 5

## 1 8 4 5

2 1 7 7 1 0

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-1. The OP ask for the way of find the values, no the answer. – dwarandae Jan 29 '13 at 6:33
Please state it in a way that's easier to understand. Even saying that $615 \times 354 = \ldots$ is much better than what you have. – Calvin Lin Jan 29 '13 at 7:51
I * N = N and N * N = N implies N=5; ans I is odd ,it may be {1, 3 7,9} since N is 5. and k * N (5) = R ;imples R is 0 ; – Nikhil Jan 29 '13 at 10:30
observe column KTN T ==> K+N=10 ; it cannot be 5+5.. if K cannot greater than 5 since adding 6 or greater will result in value greater than 10 and condition K+T+N= T fails. therefore K must be less than ; also observe 1st partial product P * K = K (+L ->carry) implies K is even and P is 6. so K can be now either 2 or 4. since 0 6 are already consumed. Now observe N(5)+P= E +(10). We know P=6; therefore E= 1; Now you know P E N K R values, do multiplication and you will get values in first partial product. which gives L=2 and from column L+R+K=T ==> T=L+5; – Nikhil Jan 29 '13 at 10:48