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
Solution To The Problem
