In a certain code, the symbol for 0 (zero) is `alpha` and for 1 is `beta`. There are no other symbols for all other numbers greater than one. The numbers greater than 1 are to be written only by using the two symbols given above. The value of the symbol for 1 doubles itself every time it shifts one place to the left. Study the following examples :
'0' is written as `alpha`
'1' is written as `beta`
'2' is written as `beta alpha`
'3' is written as `beta beta`
'4' is written as `beta alpha alpha` and so on.
Which of the following will represent the average of `beta alpha beta alpha alpha and beta alpha beta alpha` ?

Options

A. `beta alpha alpha beta`
B. `beta alpha alpha alpha`
C. `beta beta beta beta`
D. `beta beta alpha alpha`

Answer

C

Explanation

Average of 10100 and 1010.
`{:(1,0,1,0,0),(16,8,4,2,1):}`
and `{:(1,0,1,0),(8,4,2,1):}`
Adding only the numbers below the 1s, we get 16 + 4 = 20 and 8 + 2 = 10. Average of 20 and 10 is 15. Now, 15 is represented as :
`{:(15,1),(7,1),(3,1),(1,):}`
`therefore 111 = beta beta beta beta`