Find the maximum number of numbers in the sequence

From the numbers 1; 2; 3; 4; … 500 a sequence is formed by deleting
numbers so that no two remaining numbers have a sum which is a multiple
of 7. The maximum number of numbers in this sequence is_______________

I guess the Numbers in the sequnce are the Multiples of 7 beween 1 & 500.

At last there will be only 2 numbers remaining

NO...you guys are wrong...

1,2,3 is one sequence which satisfies the condition
2,3,7,8 is another sequence
similar way you have to find a sequence with maximum numbers

James,

i am not clear about the question...
Remaining two numbers means which two numbers.....?
please give some example....

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suresh

Suresh,
you have to write a sequence of numbers between 1 to 500 in such a way that o that no two numbers have a sum which is a multiple of 7.

let us say you have a sequence like this

1,2,3,4 here 3+4=7 which is a mutliple of 7. So this is an invalid sequence.
but 1,2,3 is a valid sequence since no two numbers have a sum which is a multiple of 7.

You have to find the sequence with maximum numbers...and you don't have to write the sequence. you need to find the total number of numbers in that sequence.

I hope this clears all your doubts.:)

James,

yes. it's very helpful...one more doubt...
that two numbers are only consecutive numbers or any two number..

For example...
if i write a sequence 1,2,3,5,....

In this above series no consecutive number are multiple by 7..
but if i add 5+2 = 7 which is multiple by 7..

plz clarify this one..

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suresh

If its not a consecutive numbers then the total number of numbers in this sequence is 217.

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suresh

this is nice one

Excellent Suresh...

Give your solution.

First you take 1 to 30...

the series is 1,2,3,7,8,9,10,15,16,17,22,23,24,29,30,.....

Look at the first four numbers are 1,2,3.7... So any numbers are multiply by 7 and below the three numbers of seven are not in the part of series...

example....if you take the number 21 then the numbers 18,19,20,21 are not in the series...(18+3)(19+2)(20+1)(21+7)....

this series going like this after the number 10.....

The anwer is (490/7) * 3 + 7 = 217.

(In the above answer i add 7 because the number between 1 to 10, the series have 7 numbers)

i don't know any other mathematicla formula...

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suresh