Question

LGBARIDDLE

How many unique integer solutions exist for a + b + c = 5 such that (a, b and c) \(\ge\) 0

Answer 1

an infinite number

Answer 2

no. it's finite

Answer 3

example:
1.9+1.1+2
1.99+1.01+2

Answer 4

1.999+1.001+2

Answer 5

these are just the ones im getting with 1.9.., 1.0...1, and 2

Answer 6

unless you specify that a, b and c are integers

Answer 7

uhh yeah they are integers

Answer 8

SEEE, ok now my solution doesn't work :/

Answer 9

a+b=5-c
c has to be less than or equal to 5, since a+b cannot be negative.. so now list all the choices:
c=0, a+b=5
c=1, a+b=4
c=2, a+b=3
c=3, a+b=2
c=4, a+b=1
c=5, a+b=0... now expanding on this...

Answer 10

c=0:
a=0, b=5
a=1, b=4
a=2, b=3
a=3, b=2
a=4, b=1
a=5, b=0

Answer 11

c=1:
a=0, b=4
a=1, b=3
a=2, b=2
a=3, b=1
a=4, b=0

Answer 12

wow brute force

Answer 13

6+5+4+3+2+1

Answer 14

11+7+3=11+10=21?

Answer 15

Brute force is my fave method.. I am a gorilla after all!

Answer 16

21 sets of numbers for a, b, and c. If a=0, then 6 sets for b and c (0,5 and 1,4 and 2,3 and 3,2 and 4,1 and 5,0). If a=1, then 5 sets for b and c (0,4 and 1,3 and 2,2 and 3,1 and 4,0), etc., until you get to a=5, and then there is only the set of 0,0 for b and c. Adding 6 + 5 + 4 + 3 + 2 + 1 = 21.