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Sequences and sequences.... time to tickle you brain.

Scorching goIITian

Posted on
27 Apr 2012 13:00:18 IST
Posts: 262
27 Apr 2012 13:00:18 IST
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Sequences and sequences.... time to tickle you brain.
Engineering Entrance , JEE Main , JEE Main & Advanced , nonacademic , academic , Say Hi ! , Puzzles , General Knowledge , Miscellaneous

Can you guess the rules for generating these sequences?
Note that we believe in giving people at least ten terms as a hint.
I am sure everyone likes this.So pleases click like

Source Internet

• This one was in the New York Times a while back:
2, 3, 3, 5, 10, 13, 39, 43, 172, 177, ... Give up?

• 0, 0, 0, 0, 4, 9, 5, 1, 1, 0, 55, ...
Hint: write out
one, two, three, four, five, six, seven, eight, nine, ten, eleven, ...
and think like a Roman! Give up?

• From Chess Life, said to be a sequence that the world chess champion did not guess (except we would bet he was not given 10 terms):
7, 9, 40, 74, 1526, 5436, 2323240, 29548570, 5397414549030, 873117986721660, ... Give up?

• Everyone knows about the even numbers, sequence A005843.
Less well-known are the eban numbers (the name is a strong hint!):
2, 4, 6, 30, 32, 34, 36, 40, 42, 44, 46, ... Give up?

• Somewhat in the same spirit are the emirps:
13, 17, 31, 37, 71, 73, 79, 97, 107, 113, ... Give up?

• Elegant, classic:
1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, ... Give up?

1, 3, 7, 12, 18, 26, 35, 45, 56, 69, 83, ... Give up?

Hmmm! Still thinking? I've seen nine-year-olds guess it quicker than that.

• This one is easy for smart seventeen-year-olds, or if you've seen it before, otherwise not!
2, 12, 1112, 3112, 132112, 1113122112, 311311222112, 13211321322112, 1113122113121113222112, 31131122211311123113322112, ... Give up?

John Conway's astonishing analysis of the asymptotic properties of the above sequence is well worth reading - see the reference given.

• Very easy:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25... Give up?

• Also not so hard if approached in the right way:
1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620, ... Give up?

• The "RATS" sequence!
1, 2, 4, 8, 16, 77, 145, 668, 1345, 6677, 13444, 55778, ... Give up?

Scorching goIITian

Joined: 10 Feb 2012 20:33:35 IST
Posts: 262
27 Apr 2012 13:01:29 IST
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If you didn't got the next number even after thinking a lot and is so in need of the answer to the question.You may click the five up sign to know the answer.

Scorching goIITian

Joined: 10 Feb 2012 20:33:35 IST
Posts: 262
27 Apr 2012 13:02:05 IST
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Any body has any intresting sequences may also post the sequence as comment .Likes for sure....

Scorching goIITian

Joined: 10 Feb 2012 20:33:35 IST
Posts: 262
27 Apr 2012 13:03:44 IST
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How do you think the sequences are please comment<\b> guys.

New kid on the Block

Joined: 27 Apr 2012 17:51:41 IST
Posts: 3
27 Apr 2012 17:55:56 IST
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useless article...u deserve to be called....boy who was kicked

New kid on the Block

Joined: 1 Apr 2012 12:44:25 IST
Posts: 9
1 May 2012 12:54:20 IST
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hey i got the first 1.it is 2,3,3,the sum of previous terms minus 3.... and so on.. so the next term in the question will be 461.am i right?

New kid on the Block

Joined: 1 Apr 2012 12:44:25 IST
Posts: 9
1 May 2012 13:01:11 IST
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got the 4th one too...'eban' numbers could b e-ban i.e. ban of use of 'e'. so the next one will nt be 47 nt 48 nt 49 bt it will b 50(fifty)...correct?

New kid on the Block

Joined: 1 Apr 2012 12:44:25 IST
Posts: 9
1 May 2012 13:15:29 IST
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7th ones ans is 98. it has a common differnce in its term in a AP. nt the terms are in AP bt their differnces are.... so its better to nt call it a COMMON difference

New kid on the Block

Joined: 1 Apr 2012 12:44:25 IST
Posts: 9
1 May 2012 13:18:58 IST
0 people liked this

the ans for the 8th one is 27 nt 26, the series lack of multiples of 13. :)

New kid on the Block

Joined: 1 Apr 2012 12:44:25 IST
Posts: 9
1 May 2012 13:24:08 IST
1 people liked this

and mr devendar pal singh, if u cant think , keep ur buissness away from the place where u need to workout with ur "BRAIN"

Scorching goIITian

Joined: 10 Feb 2012 20:33:35 IST
Posts: 262
1 May 2012 16:02:06 IST
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sorry @Raghav Yadav the answer to the first question you gave is wrong. look that 10 is not equal to 5+3+3-3 (the method you suggested..).If you want to know the answer click on the give up and you will get a very detailed solution

Scorching goIITian

Joined: 10 Feb 2012 20:33:35 IST
Posts: 262
1 May 2012 16:04:46 IST
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@ Raghav Yadav the solution to eban numbers is right..Great job dude.. The sequence was formulated by a mathematician.n' you have solved it.

Scorching goIITian

Joined: 10 Feb 2012 20:33:35 IST
Posts: 262
1 May 2012 16:08:10 IST
0 people liked this

Scorching goIITian

Joined: 10 Feb 2012 20:33:35 IST
Posts: 262
1 May 2012 16:10:52 IST
0 people liked this

@Raghav Yadav sorry dude your answer to 8th one is wrong...I can leave you a hint ."You are in USA and going up and up and you notice some numbers and a miss.You are idle to take the steps".

Scorching goIITian

Joined: 10 Feb 2012 20:33:35 IST
Posts: 262
1 May 2012 16:11:58 IST
0 people liked this

These are some of the greatest sequence puzzles in the world ...Try it.

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