Problem:
The symbol Rk​ stands for an integer whose base-ten representation is a sequence of k ones. For example, R3​=111,R5​=11111, etc. When R24​ is divided by R4​, the quotient Q=R4​R24​​ is an integer whose base-ten representation is a sequence containing only ones and zeros. The number of zeros in Q is
Answer Choices:
A. 10
B. 11
C. 12
D. 13
E. 15
Solution:
Since R4​R24​​=9R4​9R24​​=104−11024−1​=104−1(104)6−1​
=1020+1016+1012+108+104+1=100010001000100010001,
there are 15 zeros in the quotient.
OR
Divide to compute the quotient:
1111)​11111​00011111​00011111​00011111​00011111​00011111​​
Note that there are 5×3=15 zeros in the quotient.