Each of A, B, C and D is a positive integer with the proviso that A ≤ B ≤ C ≤ D ≤ 20.

Determine the total number of quadruplets (A, B, C, D) such that A*B*C*D is divisible by 50.

To lazy to count :

 x,20,20,20    20 sol.  since x may be any number 1,2,. 20      x,19,20,20     19 more,since x may be any number 1,2,... 19      x,18,20,20     18 more,since x may be any number 1,2,... 18     x,17,20,20     17 more,since x may be any number 1,2,... 17    
.........
1,1,20,20     1 more,since x =1     so far  210  sol.

for 15,y,19,20           5 sol for y 

for 10,y,19,20           10 sol for y,
 for 5,y,19,20           15 sol for y,   tot:     30 more
for x,y,18,20                                    27 more
for x,y,17,20                                    24 more
for x,y,16,20                                    21 more

 

for x,y,15,20                                 225 more
for x,14,14,20                                 2  x is 5 or 10

for x,13,14,20                                 2

for x,12,14,20                                 2

for x,11,14,20                                 2

for x,10,14,20                                 10  x is 1,2,...10

 etc  etc

Whoever wants to continue is welcome. I am too lazy.

 Not too much left  anyway...

 GENERALIZE, -based on the above

I  just hope there are no errors so far.

 

 

 

f0r x,y,18,20                                    27 more

 

 

Posted by Ady TZIDON on 2010-08-20 14:09:20