S =  ( 50+1 ) x 50 :2 

S = 1275

good !

20 = 2^2 x 5 

20 = 4.5 

The smallest number such that the ptoduct of all it is digit is 20 is : 45 

Good ! ^^

a, b, c have 9 nonzero digits with each of them appearing exactly once. The smallest possible number: 123 The last digit of c should be a multiple of 5 ending in 5, so the first digit of a should end in an odd digit (3, 7, or 9). The first digit of a should be 1 because if it were larger, then c would be four digits. Process of trial and error:

a: b: c =1: 3: 5 = 123: 369 : 615 3 and 6 repeated

a: b : c = 127: 381: 635 1 and 3 repeated

a: b: c = 129: 387: 645 This works!  

Answer : a=129, b = 387, c = 645. 

(1+1x)(1+1y)=32(1+1x)(1+1y)=32

⇔x+1x.y+1y=32⇔x+1x.y+1y=32

⇔x+1x=32:y+1y=3y2y+2⇔x+1x=32:y+1y=3y2y+2

⇔(x+1)(2y+2)=3xy⇔(x+1)(2y+2)=3xy

⇔2xy+2y+2x+2=3xy⇔2xy+2y+2x+2=3xy

⇔2y+2x+2−xy=0⇔2y+2x+2−xy=0

⇔2(x−2)−y(x−2)+6=0⇔2(x−2)−y(x−2)+6=0

⇔(2−x)(y−2)=−6⇔(2−x)(y−2)=−6

⇔(x−2)(y−2)=6⇔(x−2)(y−2)=6

⇒6⋮x−2⇒6⋮x−2 

But x;y be positive integer should x−2≥−1;y−2≥−1x−2≥−1;y−2≥−1

⇒x−2∈{1;2;3;6}⇒x−2∈{1;2;3;6}

⇒x∈{3;4;5;8}⇒x∈{3;4;5;8}

 y ∈ { 8;5;4;3 }

Answer : ...

⇒x∈{3;4;5;8}

 172650

The term for P is :

         (500 - 1) + 1 = 500 (skull)

Total P is : 

         (500 + 1) x 500 : 2 = 125250

So P = 125250 

1/1.5+1/5.9+...+1/1991.1995

= ( 1 - 1/5 +1/5-1/9+1/9-1/13+...+1/1991+1/1995) :4

= ( 1-1/1995) :4

= 1994/1995:4

=997/3990

answer : 997/3990

The volume of that tank is :

   2,4 x 1,5 x 1,2 = 4,32 ( m^3 )

Have : 4,32 m^3 = 4320 dm^3 = 4320 litters

Answer : the tank has 4320 litters of water !

The age of the present child is :

44 x 1/4 = 11 ( age )

The age of child when his father 60 years old is :

 11 + ( 60-44)=27 ( age )

answer : his age when his father 60 years old is 27 years old .

The sum of the sums of the above sum is:

                  (1999 - 1) : 2 + 1 = 1000 (skull)

The sum above is: 

                   (1999 + 1) x 1000 : 2 = 1 000 000

Answer : 1000000