(adsbygoogle = window.adsbygoogle || []).push({}); 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[tex]\leq[/tex]n(a is less than or equal to n)and n[tex]\leq[/tex]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.

Answer is 8.

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# Homework Help: Combinatorics(word question)

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