Question

If x = 111 ….. 1 (20 digits), y = 333 …… 3 (10 digits) and z = 222 … 2 (10 digits), then what is x- y2z equal to

Answer 1

x=1 
y=2   z=  3...9 (7 ways) 
y=3   z=  4...9 (6 ways) 
...
y=8   z=  9 (1 way) 

Total : 7+6+...+1

x=2
y=3   z=  4...9 (6 ways) 
y=4   z=  5...9 (5 ways) 
...
y=8   z=  9 (1 way) 

Total : 6+5+...+1

...

x=6
y=7  z= 8,9 (2 ways) 
y=8, z=1 (1 way)
Total : 2+1

x=7
y=8  z=  9(1 way) 

Total : 1


Required number of ways = ( 7+6+...+1) + (6+5+...+1) + (5+4+3+2+1) + (4+3+2+1) + (3+2+1) + (2+1) + 1
=28+21+15+10+6+3+1
= 84