Question

how 9999 =4, 8888=8, 1212=0​

Answer 1

The RHS represents the no. of closed figures in the numbers given in each LHS.

Consider the equation,

9999 = 4

In each 9 we can see a closed part, so there are a total of 4 × 1 = 4 closed parts, or closed figures, in the LHS. Hence the RHS.

Consider the equation,

8888 = 8

In each 8 we can see two closed parts, the upper closed part and the lower one, so there are a total of 4 × 2 = 8 closed figures in the LHS. Hence the RHS.

Consider the equation,

1212 = 0

The number 1 has no closed part as both the ends of 1 are unjoined, so has 2. Hence there are no closed figures in LHS totally. Hence the RHS.

The 10 digits and their corresponding no. of closed figures are given below.

0 = 1

1 = 0

2 = 0

3 = 0

4 = 1

5 = 0

6 = 1

7 = 0

8 = 2

9 = 1

Hence we see that,

$\displaystyle\begin {aligned}\sf {1.}\quad&\sf{9999=1+1+1+1}\\&\sf{9999=4}\\\\\sf{2.}\quad &\sf {8888=2+2+2+2}\\&\sf{8888=8}\\\\\sf{3.}\quad &\sf{1212=0+0+0+0}\\&\sf{1212=0}\end {aligned}$