What are all the possible solutions to this math problem?

Question

Hello, I have this problem: a + b + c + d + e = 69;

a = greater than or equal to 20 but less than or equal to 25;

b = greater than or equal to 22 but less than or equal to 32;

c = greater than or equal to 8 but less than or equal to 18;

d = greater than or equal to 4 but less than or equal to 9;

e = greater than or equal to 0 but less than or equal to 4.

What are all the possible solutions to this?

Answer 1

There are 662 possible solutions...

I wrote a short program in C++ to find them all and

dumped the results into a text file which, along with

the code, is posted in the RESOURCES section under

this link.

Go to the RESROUCES section to find it!!

Here are the first few...

A=20 : B= 22 : C=14 : d = 9 : e = 4

A=20 : B= 22 : C=15 : d = 8 : e = 4

A=20 : B= 22 : C=15 : d = 9 : e = 3

A=20 : B= 22 : C=16 : d = 7 : e = 4

A=20 : B= 22 : C=16 : d = 8 : e = 3

A=20 : B= 22 : C=16 : d = 9 : e = 2

A=20 : B= 22 : C=17 : d = 6 : e = 4

A=20 : B= 22 : C=17 : d = 7 : e = 3

A=20 : B= 22 : C=17 : d = 8 : e = 2

A=20 : B= 22 : C=17 : d = 9 : e = 1

A=20 : B= 22 : C=18 : d = 5 : e = 4

A=20 : B= 22 : C=18 : d = 6 : e = 3

A=20 : B= 22 : C=18 : d = 7 : e = 2

A=20 : B= 22 : C=18 : d = 8 : e = 1

A=20 : B= 22 : C=18 : d = 9 : e = 0

A=20 : B= 23 : C=13 : d = 9 : e = 4

A=20 : B= 23 : C=14 : d = 8 : e = 4

....

Here are the last few...

....

A=25 : B= 29 : C=10 : d = 5 : e = 0

A=25 : B= 29 : C=11 : d = 4 : e = 0

A=25 : B= 30 : C=8 : d = 4 : e = 2

A=25 : B= 30 : C=8 : d = 5 : e = 1

A=25 : B= 30 : C=8 : d = 6 : e = 0

A=25 : B= 30 : C=9 : d = 4 : e = 1

A=25 : B= 30 : C=9 : d = 5 : e = 0

A=25 : B= 30 : C=10 : d = 4 : e = 0

A=25 : B= 31 : C=8 : d = 4 : e = 1

A=25 : B= 31 : C=8 : d = 5 : e = 0

A=25 : B= 31 : C=9 : d = 4 : e = 0

A=25 : B= 32 : C=8 : d = 4 : e = 0