Long division with zero to nine substitution

[K Sengupta]

Substitute the letters by a different digit from 0 to 9 to satisfy this cryptarithmic long division problem.

....N K T
...-------------------
F A R |...F R M N K B
...A K K N
...---------------------
..... A B I K
...AM O K
...---------------
.....R T I B
.....R A K T
...-------------
.....R A F

Note:

(i) None of F, N, A and R can be 0.

(ii) All the dots are posited with a view to facilitate the formatting, and none of the said dots represent decimal points, or correspond to any arithmetic operations.

 

[davee123]

Actually, I think that as long as you state that none of the letters represent the *same* digit, you don't need to give the hint about which ones aren't 0. Figuring out which is 0 is pretty simple.

Spoiler

A = 2
B = 7
F = 3
I = 0
K = 8
M = 5
N = 9
O = 6
R = 1
T = 4

DaveE

 

[Architeuthis Dux]

I would recommend approaching this problem by breaking it down into smaller parts and using logic to find a solution. Here are some steps that could be followed:

1. Start by identifying which letters can potentially represent the same digit. For example, in the first line, N and K are both in the same position and could potentially represent the same digit.

2. Use the given restrictions to narrow down the possibilities. None of the letters F, N, A, and R can be 0, which means that these digits must be used in the remaining positions.

3. Use the fact that the division must be correct to eliminate some possibilities. For example, in the first line, if N and K represent the same digit, then the result of dividing F by N must be a whole number. This can help narrow down the possibilities for N and K.

4. Use trial and error to test different combinations and see if they satisfy the given equations. Keep in mind that some combinations may work for one equation, but not for the others. Keep refining the possibilities until a solution is found.

5. Use logic and patterns to find the solution. For example, in the third line, the result of dividing AM by O must be a whole number. This can help narrow down the possibilities for O.

Overall, this problem requires a combination of logical thinking, trial and error, and pattern recognition to find a solution. As a scientist, it is important to approach problems like this systematically and to use evidence and reasoning to support any conclusions.