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According to given condition here, we need to check sum of 2 diagonal elements is lesser or equal to its 2 (upper and left) neighbor

A[i,j] + A[i+1,j+1] <= A[i,j+1] + A[i+1,j]

6 + b <= 34 + 7 , hence b < = 35

34 + d  < = 13 + b ( to keep everything minimal LHS should be minimal, Hence d =1)

34 + 1 <= 13 + b (b = 22)

22 + a <= 32 + 7 ( a<= 17)

7 + c <= b+a

7 + c <= 22 + a ( a = 7, c = 22)

b + e <= d+c

22 + e <= d + 22 (e =1, d =1) (To keep everything minimal)

Hence a=7, b=22, c=22, d=1, e=1

a + b + c + d + e = 7 + 22 + 22 + 1+ 1 = 53

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In cross sum puzzle value can't be zero or negative
and we have to minimize a, b, c, d, e so we will choose minimum possible values

given that for any 2 $\times$ 2 matrix (sum of diagonal elements) $\leq$ (sum of non diagonal elements)

consider, 34 + d $\leq$ 13 + b
choose minimum value for d = 1 then b must be atleast b = 35 - 13 = 22 
here we cant choose b = 1, doing that will caz LHS to be greater

consider, b + e $\leq$ d + c
22 + e $\leq$ 1 + c

choose minimum value for e = 1 then c must be atleast c = 23 - 1 = 22 
here we cant choose c = 1, doing that will caz LHS to be greater

now for a
consider, 7 + c $\leq$ b + a
7 + 22 $\leq$ 22 + a
7 $\leq$ a

choose minimum value for a = 7

So, answer to this ques will be a + b + c + d + e = 7 + 22 + 22 + 1 + 1 = 53 

0 0 votes
A. The ques is wrong, as arr(0,1)+arr (1,2) {23+7} is greater than arr (0,2)+arr (1,1){22+6} which violates the base condition.

 

B. The ans cannot be computed by some specific method, because this will lead to a system of 4 variable inequality.

On the bases on hit and Try, I can say that 53 should be the correct ans.
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