Chittagong-2014

For students of class 9-10 (age 14-16)
Mahfuz Sobhan
Posts:25
Joined:Sat Feb 07, 2015 5:40 pm
Chittagong-2014

Unread post by Mahfuz Sobhan » Thu May 28, 2015 8:29 pm

Everyday, a fox catches 5 crocodiles and locks them in a cave. Every day, he takes
one of the crocodile randomly, and tells, “If you can part the crocodiles into seven,
I will free you and eat the rest of the crocodiles. But if you can’t, I will eat you and
leave the rest alive but captive.” If the month is of 31 days, how many crocodiles
will be there in the cave after one month?

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seemanta001
Posts:13
Joined:Sat Jun 06, 2015 9:31 am
Location:Chittagong

Re: Chittagong-2014

Unread post by seemanta001 » Sat Jun 06, 2015 5:20 pm

The answer is 17.
If a crocodile cannot part the others into 7 then everyday there are 4 new crocodiles added on. So, firstly, we have to find the minimum of n when 4n divisible by 7. Here n = 7. So, on the 7th day a crocodile will be able to part the others into 7. Thus, on the 8th day there will be only 1 crocodile remaining.Now we have to find the minimum of n when 4n + 1 divisible by 7. Here n = 5; There are another 24 days in the month . So, we can say that after 5 * 4 or 20 more days, on the (7 + 20)27th day, again there will be only 1 crocodile remaining.Hence, after 31 days, there will be 17 crocodiles remaining.

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