Question

Help this question below. (cant type in here)

Answer 1

hint : there is a digit '0' in each number

Answer 2

scratch that, from 211... changes story..

Answer 3

\[\Pi(200)\rightarrow \Pi(209) \] and number with '0' will be ignored. So how???

Answer 4

2*1*1 + 2*1*2 + ..... 2*1*9
+
2*2*1 + 2*2*2 + ..... 2*2*9
...
2*9*1 + 2*9*2 + ..... 2*9*9

Answer 5

we need to cnsider oly above sum of products right ?

Answer 6

factor 2*1, 2*2.... from each row

Answer 7

2*1[1 + 2 + ..... 9]
+
2*2[1 + 2 + ..... 9]
...
2*9[1 + 2 + ..... 9]

Answer 8

1+2+... +9 = 9*10/2 = 45
factor it as well

Answer 9

and factor the 2 as well

Answer 10

2^9*45[1+2+.... +9]

2^9*(45)^2

Answer 11

The expression can be expressed as:
\[2.0.0+2.0.1+..2.0.9+2.1.0+2.1.1+...2.1.9+..+2.9.0+2.9.1+...+2.9.9+3.0.0\]
Which can be rearranged as:\[2.0.(0+1+..+9)+2.1.(0+1+...+9)+...2.9.(0+1+..+9)+3.0.0\]
Which can be further arranged as:\[2.(0+1+...+9).(0+1+...+9)=2.45.45=4050\]

Answer 12

Thanks!