 # Algorithms ME Question

#1

#2

a = 7; b = 22; c = 22; d = 1; e = 1 ----> Total = 53

#3

#4

Solution:

Since we need to find the minimum sum and it is clearly said in the question that a, b, c, d, e are all positive integers so we proceed in the following way:
First form equations:
d + 34 <= b + 13 -----------------(i)
b + 6 <= 7 + 34 ------------------(ii)
a + 22 <= 32 + 7 ----------------(iii)
c + 7 <= a + b ------------------- (iv)
b + e <= c + d --------------------(v)

from equ. (ii), we get => ( b <= 35 )
from equ. (i), we get => ( d <= b - 21)
We know that smallest value possible for d is 1.
S0, we get: d = 1; b = 22 ( value of b satisfies equ (ii) ).

Now, substitute the value of b and d in equ. (v), we get e <= c - 21
We know that smallest value possible for e is 1.
S0, we get: e = 1; c = 22

Now, from equ. (iii), we get => ( a <= 17 )
On substituting the values of b and c in equ. (iv), we get ( a = 7 )

Hence we get the above answer.
a = 7; b = 22; c = 22; d = 1; e = 1 ----> Total = 53

#5

thanks …