Find the missing numbers in this sequence. There are only these 12 terms, in order, which do not directly depend on each other:

43, 34, 111, 110, ?, 132, 133, ?, 33, 43, ?, 37

We denote the letters in the nth month in the year as f(n) and the number of days in the nth month as g(n).

Then, the given series s(n) =(g(n))_(base f(n).

f(1) = # letters in January = 7, and g(1) = 31

We know that the decimal number 31 is written as 43 in base 7.

Hence, s(1) = 43

Now, s(5) = (31)_10 = (1011)_3

s(8) = (31)_10 = (51)_6

s(11) = (30)_10 = (36)_8

Consequently, the missing terms in order, are respectively 1011, 51 and 36.

*Edited on ***November 22, 2007, 10:33 am**