I am carrot +_+

We have a magical carrot multiplier machine, which multiplies an input carrot into at most 6 carrots, and minimum just 1 (gives the carrot back). But it can multiply only original carrots, the ones which were not put into the machine ever.

There are 286 286 carrots of 143 143 different shades such that there are exactly 2 2 carrots of each shade. All of these carrots after treating with the machine, are filled in a bag.

There are 1 1 n 11^n different compositions possible for this bag. Find n n .


Details and Assumptions :-

\bullet The carrots formed by multiplying one particular carrot are identical (due to magic of the multiplier).

\bullet The 143 143 different shades are well distinguishable, no 2 look alike.


This problem is a part of the set Vegetable Combinatorics


The answer is 143.

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1 solution

Aditya Raut
Mar 3, 2015

Just look at the possible number of carrots of a particular color in the bag.

The bag will have at least 2 carrots of any given color (If both of them were given back by machine), and maximum 12 carrots of any given color (If both of them were multiplied to 6).

Thus there are 11 11 different contributions possible from a given color for the bag.

We have 143 colors, so by rule of product , there will be 1 1 143 11^{143} compositions for the bag. n = 143 \boxed{n=143}

Is the question not over rated?

The solution is simple.

Janardhanan Sivaramakrishnan - 6 years, 3 months ago

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Yes, I too feel it's overrated, but that happens because when there's some little trick in the question, people make tiny mistakes and give attempts, if the attempts are wrong, due to the rating system the rating of problem increases... Nothing I could change :(

Aditya Raut - 6 years, 3 months ago

Nice question Aditya :)

Also, did you get that mail that I had sent to you , a little while ago ?

A Former Brilliant Member - 6 years, 3 months ago

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@Agnishom Chattopadhyay , @Prasun Biswas , @Pranjal Jain

Lovely question , don't you think !! :)

A Former Brilliant Member - 6 years, 3 months ago

I'm terribly sorry :( I haven't logged in to the gmail account since a while, so I didn't see it before (Seen now). From now I'll make sure I check the mails there periodically. Apologies @Azhaghu Roopesh M

Aditya Raut - 6 years, 3 months ago

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Thanks a lot for helping out :)

No worries bro ! It's just that no other moderator was interested and I had also tried contacting Calvin sir and I had got no response from him too and that was when I came across your profile and your email id .

Thanks again !

A Former Brilliant Member - 6 years, 3 months ago

Well.. Aditya I was confused between most and minimum multiplier. i was thinking there could be 2,3,4 and 5 also possible. Nice solution..

Bhupendra Jangir - 6 years, 3 months ago

Nice question @Aditya Raut . What's your score at INMO?

Aditya Kumar - 6 years, 3 months ago

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It's 57, maybe it's not enough to get to next level ... Let's see.... What was yours?

Aditya Raut - 6 years, 3 months ago

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Congrats bro! Enjoy your camp.

Aditya Kumar - 6 years, 3 months ago

Actually I didn't give INMO but my friend got 46

Aditya Kumar - 6 years, 3 months ago

It is I who got 46,...how many people do you know who got more than 50....and anyways, you will clear the exam...so don't worry..

Abhishek Bakshi - 6 years, 3 months ago

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@Abhishek Bakshi Amazing spirit of yours. Nice try :). You may try for a revaluation. Better luck next time:)

Aditya Kumar - 6 years, 3 months ago

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@Aditya Kumar No next time for me...and have already given for re-evaluation..

Abhishek Bakshi - 6 years, 3 months ago

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