# Algorithms ME Question

**Anmol_Binani**#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**