Given equation x + y + z = n where n is a positive integer number that user can input, write a program to print out all possible solutions (x, y, z) such that x, y, and z all are positive integer and the total number of the solutions.

Example: n = 3 (1, 1, 1) is the only solution n = 4: (1, 1, 2), (1, 2, 1), (2, 1, 1) , total solutions = 3

Solution submitted by Dzeng at April 9, 2020, 11:52 p.m.

```
def solution1():
#change n for different numbers
n = 0
x = 1
y = 1
z = 1
set1 = []
solutions = []
count = 0
finished = False
while finished == False:
if x + y + z == n:
count += 1
set1 = [x, y, z]
solutions.append(set1)
if y < (n-1) and z > 1:
y += 1
z -= 1
elif x < n-2:
x += 1
y = 1
z = 1
else:
finished = True
else:
z += 1
print("There are", count, "solutions, and the solutions are", solutions)
#solution1()
def equation_2(n):
count = 0
ret =list()
for x in range(1, n):
ret.append((x, n-x))
count +=1
return (count, ret)
def main():
n = int(input("Enter Number:"))
count = 0
solutions =list()
for x in range(1, n-1):
sol = equation_2(n-x)
count += sol[0]
for a in sol[1]:
solutions.append((x, a[0], a[1]))
print("There are", count, "solutions, and the solutions are", solutions)
#main()
def solution2(n):
return [(x,y,z) for x in range(1, n-1) for y in range(1, n-x+1) for z in range(1,n-x-y+1) if x+y+z == n]
#print(len(solution2(30)))
```

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