This Might Be A Hard Problem. Just Might.

Probability Level 4

If $X$ is a finite set, let $|X|$ denote the number of elements in $X$ . Call an ordered pair $(S, T)$ of subsets of ${1,2,\dots,n}$ admissible if $s>|T|$ for each $s \in S$ , and $t > |S|$ for each $t \in T$ . How many admissible ordered pairs of subsets of ${{1,2,\dots,10}}$ are there?

The answer is 17711.

1 solution

Vishruth Bharath
Jan 22, 2018

If you wanted to, you could prove the whole scenario, which would also give you the answer. However, let's work smarter. We can see that we are dealing with Fibonacci Numbers, which gives us a huge leap in the problem. The question asks us to find the number of admissible ordered pairs of subsets of the set ${1,2,\dots, 10}$ . This equals the 22nd Fibonacci number, which is $F_{22}=\boxed{17711}$ .

Sorry,sir.I failed to figure out why the problem is related to Fibonacci Numbers.Would you mind giving more details of the solution?

Haosen Chen - 3 years, 1 month ago

This Might Be A Hard Problem. Just Might.

The answer is 17711.

1 solution

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