# Combinatorics(word question)

1. Mar 16, 2010

### jjangub

1. The problem statement, all variables and given/known data
What is the number of positive integers n satisfying the property that the number b of positive integers a satisfying the property that a$$\leq$$n(a is less than or equal to n)and n$$\leq$$a^2(n is less than or equal to a^2) satisfies the property that the number of possible ways we can put 3 different objects into b different boxes is at least as big as the number of 0,1 sequences of length n.

2. Relevant equations
3 different objects into b different boxes = b^3
number of 0,1 sequences of length n = 2^n

3. The attempt at a solution
From the question, we know n is between a and a^2.
n is the number of positive integers
a is the positive integers before n
b is the number of a
and we know that b^3 is greater or equal to 2^n
if we try n=1, then a=1, b=1
n=2, then a=1,2, b=2
n=3, then a=1,2,3, b=3...
therefore n=b, which gives n^3 is greater than or equal to 2^n.
I don't know how to get n in other way, so I tried until n=10.
if n=10, then a=1,2,3,4,5,6,7,8,9,10, b=10
then 10^3 is not greater or equal to 2^10.
Therefore n is between 2 and 9 since if n=1, then a=1, b=1
1^3 is not greater of equal to 2^1.