Puzzle #115: The First Rabbit

This is a puzzle I got recently from my daughter, Anisha, who in turn got this puzzle from Alok Mittal’s Mathematical Circles Class.

There is an island on which a rabbit arrives. Rabbit reproduces, as part of which it gives birth to other rabbits. No rabbit dies on the island and not all rabbits have to reproduce. The way they reproduce is as follows:

  • Grey rabbit gives birth to a grey and a white
  • Spotted gives broth to grey and white
  • White gives birth to all three

No rabbit has died and not all rabbits have to reproduce

Grey – 40; spotted 30 and White is 40

What color is the first rabbit?

Happy figuring out!

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9 Responses to Puzzle #115: The First Rabbit

  1. Lovely puzzle. I am so much impressed that i have shared it already to my own facebook and twitter profile. My answer is – the color of the 1st rabbit is spotted. Now i am looking forward for the reply.

  2. Chandu Karan says:

    Spotted should be the first.

  3. Garima says:

    For me the answer seems to be ‘Spotted’ because every rabbit that reproduces gives birth to a grey and a white rabbit, so if the first rabbit was either grey or white there would be a difference of 1 between the final counts for these two colors.

  4. Praneeth Kumar says:

    Spotted

  5. Prakhar says:

    I am guessing it will be spotted because if we start with a grey or a white, we may have an extra g or w, given that g and w are produced in every birth. So we may not get a situation where g = w = 40. With s to begin with, this may not be the issue.

  6. Anshul says:

    Spotted.
    G: g+s+w =40
    W: g+s+w =40
    S: w+1=30
    sinc G=W, first rabbit must be spotted.

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