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Senior | Next Rank: 100 Posts
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by Jinglander » Sun Aug 08, 2010 2:12 pm
Ok we are told both x and y are posative and greater than 1. also x+3y<1000. what is the maximum number the sum of the lengths x and y can be
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by Rahul@gurome » Sun Aug 08, 2010 5:29 pm
Jinglander wrote:Ok we are told both x and y are posative and greater than 1. also x+3y<1000. what is the maximum number the sum of the lengths x and y can be
The length of a number is the maximum if it is made of prime nos.
So, let us put x = 2, then 2^9 = 512, which is the maximum power of 2 that we can take here as 2^10 = 1,024.

Next put y = 2^7 = 128, which gives 3y = 3*128 = 384

Then 512 + 384 = 896 < 1000
Therefore, maximum length = 9 + 7 = 16
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