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Give the red ball with x

Blue ball = x5 red ball

X + 1

5x - 3

X + 1 = 1/3 (5x - 3)

3x + 3 = 5x - 3

5x - 3 - 3x - 3 = 0

2x - 6 = 0

X = 6: 2 = 3 (red ball)

3 x 5 = 15 (blue ball)

Answer: 3 red balls

              15 green balls
 

There are 162 numbers from 1 to 200 do not have the digit 2

b3 = 3375 = 153 => b = 15 => a = 13 ; c = 17 => ac = 221

We have : a ≤ ≤ c + 2 b + 1 ≤ ≤ c + 2 c + 2 = c + 2 => a + b + 1 + c + 2 ≤ ≤ c + 2 + c + 2 + c + 2 => (a + b + c) + (1 + 2) ≤ ≤ 3c + 6 => 1 + 3 ≤ ≤ 3c + 6 => 4 ≤ ≤ 3c + 6 => − 2 3 −23 ≤ ≤ c => Minc = − 2 3 −23 => a + b +( − 2 3 −23) = 1 => a + b = 5 3 53 With a = b + 1 => a + b = 5 3 53 => b + 1 + b = 5 3 53 => b = 1 3 13 => a = 4 3 43 (1) With a < b + 1 => b + 1 + b < 5 3 53 => b < 1 3 13 => a < 4 3 43 (2) From (1) and (2) => b ≤ 1 3 ≤13 and a ≤ 4 3 a≤43 So the smallest value of c = − 2 3 −23 When b ≤ 1 3 ≤13 and a ≤ 4 3

We have : 

2a+b+c+da=a+2b+c+db=a+b+2c+dc=a+b+c+2dd2a+b+c+da=a+2b+c+db=a+b+2c+dc=a+b+c+2dd

⇒2a+b+c+da−1=a+2b+c+db−1=a+b+2c+dc−1=a+b+c+2dd−1⇒2a+b+c+da−1=a+2b+c+db−1=a+b+2c+dc−1=a+b+c+2dd−1

⇒a+b+c+da=a+b+c+db=a+b+c+dc=a+b+c+dd⇒a+b+c+da=a+b+c+db=a+b+c+dc=a+b+c+dd

+> If a + b + c + d ≠0≠0

=> a = b = c = d (Because the same of namerator)

=> M = 1 + 1 + 1 + 1 = 4

+> If a + b + c + d = 0

=> a + b = -(c + d)

      b + c = -(a + d)

      c + d = -(a + b)

      a + d = -(b + c)

Change this into M , we have :

M=a+bc+d+b+cd+a+c+da+b+a+db+cM=a+bc+d+b+cd+a+c+da+b+a+db+c

M=−(c+d)c+d+−(a+d)a+d+−(a+b)a+b+−(b+c)b+c=(−1)+(−1)+(−1)+(−1)=−4M=−(c+d)c+d+−(a+d)a+d+−(a+b)a+b+−(b+c)b+c=(−1)+(−1)+(−1)+(−1)=−4

So M = 4 and M = -4

20172014

We have: 

⇒a=2017n−2016b⇒a=2017n−2016b

We have: 2a+2015b=2(2017n−2016b)+2015b=2.2017n−2017b⋮2017

We have: 

⇒a=2017n−2016b⇒a=2017n−2016b

We have: 2a+2015b=2(2017n−2016b)+2015b=2.2017n−2017b⋮20172a+2015b=2(2017n−2016b)+2015b=2.2017n−2017b⋮2017

Same as above. We hava: ⎧⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩3a+2014b=3.2017n−2.2017b⋮20174a+2013b=4.2017n−3.2017b⋮2017...2015a+2b=2015.2017n−2014.2017b{3a+2014b=3.2017n−2.2017b⋮20174a+2013b=4.2017n−3.2017b⋮2017...2015a+2b=2015.2017n−2014.2017b

So that: A⋮2017.2017...2017A⋮2017.2017...2017

⇒A⋮20172014