This is a puzzle which I told to my classmates during a talk, a few days before. I did not represent it as a puzzle, but a talk suggesting the importance of Math in general life. This is partially solved for me and I hope you will run your brain-horse to help me solve it completely. If you didn’t notice, this puzzle is not a part of A Trip To Mathematics series. Puzzle which I discussed in the talk was something like this:

“Let I have seven fishes in a huge tank of water —four male and three females. Those were allowed to sex independently but under some conditions. One male is allowed to have intercourse with female, unless other has done so. A male can have intercourse with any number of female fishes possible. If we assume that first female fish could give 100 eggs, second female fish could give 110, third 90. We are also known that a female fish might lay eggs in 21 days since the date of sex with male. The children fish are reproductive only after those are 30 days old. In each bunch of children fish of individual female fish, 60% die. In remaining 40% child fishes, the ratio of male and female is 3:2. If two fishes (male and female) can not do intercourse with each other if those are born to same mother fish, one male is allowed to have intercourse with female, unless other has done so, a male can have intercourse with any number of fishes possible, every three female fishes lay eggs in order of 100,110 and 90 eggs out of which only 40% remain alive having a ratio of male and females of 1:1 and the same rule applies to third, fourth and consecutive generations of fishes; then find the number of total fishes in my tank after one year (365 days).”

I have done many proof-reads of this puzzle and found it valid. Your comments, your ideas and suggestions might help me working more rigorously on this puzzle. This puzzle is neither too hard nor too easy. I will be updating this post frequently as my work on this puzzle is directed towards a correct way.

Total
0
Shares


Feel free to ask questions, send feedback and even point out mistakes. Great conversations start with just a single word. How to write better comments?
12 comments
  1. That is well planned. I am sure that there are more than one ways to approach at this problem –Its solution requires Probability (primarily) and Number Theory. There is a fact behind why I chosen 100, 110 and 90 eggs as fertility factors of fish: First of all I assumed that one average fish (of that species) can lay approx 100eggs. But is that really possible to have same fertility factors? I assumed one’s being exact but others (not being exact). Since It was a practical problem, I could not take $ 100+epsilon_1$ and $ 100-epsilon_2$…..
    I am not a proability geek, so I am studying some books and research papers on Population Distribution. Hope it will work.

    1. Hmm, I’m wondering how you would apply number theory in this problem…

      In any case, since you did not specify it in the question, can I assume that the time at which a male mates with a female is exactly when he reaches sexual maturity or is the time Poisson with some parameter lambda?

      This would make modeling the population much more difficult, although a bit more realistic.

      1. I need to specify few more restrictions. The morality of parent fishes.

        can
        I assume that the time at which a male mates with a female is exactly when he reaches sexual maturity or is the time Poisson with some parameter lambda?

        Not sure about it. Let me solve this puzzle using intuition and then adjust puzzle according to it.

        (sorry for late reply! Your comment was caught into spam.)

      2. About use of Number Theory:
        When solving this problem using sketch diagrams of numbers, I got some interesting pattern..which lead me to think that there might be something in NT which can helo me solve this.

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

You May Also Like

381654729 : An Interesting Number Happened To Me Today

You might be thinking why am I writing about an individual number? Actually, in previous year annual exams, my registration number was 381654729. Which is just an ‘ordinary’ 9-digit long number. I never cared about it- and forgot it after exam results were announced. But today morning, when I opened “Mathematics Today” magazine’s October 2010, page 8; I was brilliantly…

Real Sequences

Sequence of real numbers A sequence of real numbers (or a real sequence) is defined as a function $ f: \mathbb{N} \to \mathbb{R}$ , where $ \mathbb{N}$ is the set of natural numbers and $ \mathbb{R}$ is the set of real numbers. Thus, $ f(n)=r_n, \ n \in \mathbb{N}, \ r_n \in \mathbb{R}$ is a function which produces a sequence…

When nothing is everything in Set theory

In an earlier post, I discussed the basic and most important aspects of Set theory, Functions and Real Number System. In the same, there was a significant discussion about the union and intersection of sets. Restating the facts again, given a collection $ \mathcal{A}$ of sets, the union of the elements of $ \mathcal{A}$ is defined by $ \displaystyle{\bigcup_{A \in…

Mathematical Logic – The basic introduction

What is Logic? If mathematics is regarded as a language, then logic is its grammar. In other words, logical precision has the same importance in mathematics as grammatical accuracy in a language. As linguistic grammar has sentences, statements— logic has them too. After we discuss about Sentence & Statements, we will proceed to further logical theories . Sentences & Statements…

Euler’s (Prime to) Prime Generating Equation

The greatest number theorist in mathematical universe, Leonhard Euler had discovered some formulas and relations in number theory, which were based on practices and were correct to limited extent but still stun the mathematicians. The prime generating equation by Euler is a very specific binomial equation on prime numbers and yields more primes than any other relations out there in…

How Genius You Are?

Let have a Test: You need to make a calculation. Please do neither use a calculator nor a paper. Calculate everything “in your brain”. Take 1000 and add 40. Now, add another 1000. Now add 30. Now, add 1000 again. Add 20. And add 1000 again. And an additional 10.   So, You Got The RESULT!  Quicker you see the…