so big series

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Zahin Hasin Rudro
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so big series

Unread post by Zahin Hasin Rudro » Wed Jul 15, 2015 2:26 pm

A new series is to be created after erasing some numbers from the series 1, 2, 3,
4…………. 400, in such a way so that the sum of any two numbers from the series
are not divisible by 7. What is the maximum number of terms to be found in new

source:2014 dhaka ancholik, junior

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Re: so big series

Unread post by Ittesaf_Ithun » Sat Dec 26, 2015 6:22 pm

bhai jan the ans will be probably 2....... :D :lol: :lol: :x :x :x :x :twisted: :twisted: :twisted:
from iftehazyeasir

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Location: Dhaka,Bangladesh

Re: so big series

Unread post by thczarif » Wed Dec 20, 2017 3:16 pm

We can divide all the numbers in 7 parts as (mod 7),7n,7n+1,7n+2,7n+3,7n+4,7n+5,7n+6.
now see, 7n+1+7n+6=14n+7,7n+2+7n+5=14n+7 and if we take those number which are 1(mod 7) we cannot take those which are 6(mod 7) and so on.
there are floor of (400-1)/7 or 57 numbers from 1 to 400 which are 1 (mod 7)
floor of (400-2)/7 or 56 numbers of 2(mod 7)
floor of (400-3)/7 or 56 numbers of 3 (mod 7). But see if we take a number which is 0 (mod 7) there is no number which can make a sum divisible by total =57+56+56+1=170.

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