3x3 square and common sum puzzle

[K Sengupta]

Substitute each of the capital letters by a different digit from 0 to 9, such that each of the columns, each of the rows and each of the two main diagonals of this 3x3 square have the common sum LRK. It is known that L is nonzero and, each of the numbers in the nine cells contains non leading zero.

CL     RO     OR
EK     HS     AA
KE     KB     SH

 

[Edgardo]

Assuming that you mean LRK = 100*L + 10*R + K and not the product L*R*K I get:

Spoiler

a = 2 b=0 c=3 e=9 h=5 k=4 l=1 o=6 r=7 s=8
lrk=174

31 76 67
94 58 22
49 40 85

 

[Architeuthis Dux]

I find this puzzle to be an interesting mathematical challenge. The goal of the puzzle is to find a solution that satisfies the given conditions, which is to substitute each capital letter with a different digit from 0 to 9. This solution should result in a 3x3 square where each column, row, and main diagonal have the same sum, denoted as LRK. Additionally, the number in each cell should not have a leading zero.

To solve this puzzle, we can approach it by breaking it down into smaller parts. First, we can focus on finding the value of L, since it is given that L is nonzero. We can then use this value for L to find the values of R and K, since they are part of the common sum LRK.

Next, we can work on finding the values for the remaining letters, C, O, E, H, S, A, and B. We can use trial and error or a systematic approach to find the appropriate values that satisfy the given conditions. For example, we can start by assigning values to C, O, and E, and then use those values to find the values for H, S, A, and B. We can continue this process until we have a solution that satisfies all the conditions.

Overall, this puzzle requires a combination of mathematical thinking, problem-solving skills, and patience. It is a fun and challenging way to exercise our logical and analytical abilities. I encourage others to try this puzzle and see if they can find a solution that meets all the given criteria.