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        riddles >> easy >> Sneaky Sequences
        
(Message started by: Sir Col on Jun 3^rd, 2003, 10:09am)

Title: Sneaky Sequences
Post by Sir Col on Jun 3^rd, 2003, 10:09am

Some devlishly difficult sequences to investigate, and please, reasons MUST be given.

1. What is the next letter in the sequence: M, Y, V, S, E, H, M, S, ... ?

2. What is the next number 2-digit number in the sequence: 14, 91, 62, 53, 64, 96, 48, ... ?

3. Which number comes next in the sequence: 3, 7, 10, 11, 12, ... ?

4. What letter can replace the asterisk (*) in the following sequence? A, A, A, A, *, A, A, A, A, A, A (the answer is not A!)

Title: Re: Sneaky Sequences
Post by TenaliRaman on Jun 3^rd, 2003, 11:10am

4>
[Hide]
i am not sure with this but ... here it goes

it seems that the A's stands for affirmative.So there is some question and answer series going on for which there is a series of A's.Now the place where it is blank it could be A or N(for negative).Since it is not A my guess is N

[/Hide]

Title: Re: Sneaky Sequences
Post by Sir Col on Jun 3^rd, 2003, 11:59am

Incredibly, you got the right answer for #4, TenaliRaman, but for completely the wrong reason! ;D

Title: Re: Sneaky Sequences
Post by Leonid Broukhis on Jun 3^rd, 2003, 2:25pm

1> Reading in Russian: MY = We, VSE = All; in Russian the verb 'to be' is omitted in present tense, so the phrase means "We all [are] HMS...". The structure implies plural,
that is "We all are HMSes" (Her Majesty Ships, I assume);
in Russian the plural in this case would be denoted by Y.

2> [hide]11[/hide] Who cares about punctuation?

3> [hide]17[/hide] E-e-e haw!

Title: Re: Sneaky Sequences
Post by Sir Col on Jun 3^rd, 2003, 3:29pm

Wow! Not speaking Russian, I'll have to take your word for it, Leonid Broukhis. However, despite your amazing insight, it would suggest that it is not the sequence that I had in mind; care to try again?

You're spot on with #2 and #3, and your clever comment indicates that YOU know the pattern for #3.

Now, to add to the correct answers, we need fuller explantions.

Title: Re: Sneaky Sequences
Post by TenaliRaman on Jun 4^th, 2003, 8:13am

Well i got atleast the answer right for #4!!!! (yippee,hurray .... sounds of trumpets rejoicing)
But then i would like to know what is the reason behind the answer.

For #3,i did a bit of cheat.
i checked the online ....[Hide]Integer Sequence[/Hide] (http://www.research.att.com/~njas/sequences)

Title: Re: Sneaky Sequences
Post by Sameer on Aug 4^th, 2003, 3:10pm

Does the 4th one refer to Acknowledge and Negative Acknowledge associated with computer communications??

Can someone give hints for first 3 ... seems like my head is banging from all sides.. no clues to answers..

Title: Re: Sneaky Sequences
Post by Sameer on Aug 4^th, 2003, 3:19pm

Ok I figured out the first one... hope i am write

[hide] These are the first and last alphabets of planets in order so
Mercury = M Y
Venus = V S
and so forth
so the next letters are

J,R,S,N,U,S,N,E,P,O

question is.. what year we are talking because then last two pairs need to interchange ;D [/hide]

Title: Re: Sneaky Sequences
Post by Sir Col on Aug 4^th, 2003, 4:36pm

That's the ticket for #1, Sameer; and, of course, you're right about the last two.

That just leaves #4. The answer is ::[hide]N[/hide]::, as has been guessed correctly; however, no one has got anywhere near the right reason. In which case, you couldn't possible work out the next few terms.

Title: Re: Sneaky Sequences
Post by Icarus on Aug 4^th, 2003, 5:21pm

on 06/04/03 at 08:13:53, TenaliRaman wrote:

For #3,i did a bit of cheat.
i checked the online ....[Hide]Integer Sequence[/Hide] (http://www.research.att.com/~njas/sequences)

I tried that, but the answer it gives for 3, 7, 10, 11, 12 is "the location of the n^th zero in the sequence obtained by juxtaposing the binary expansions of the Fibonicci numbers."

The next value in this sequence is 15 - not the value given by Leonid which Sir Col has already declared correct.

Title: Re: Sneaky Sequences
Post by Sir Col on Aug 4^th, 2003, 6:28pm

Ah, I never thought of checking the database. Leonid's answer is correct and, as always, his clues are very subtle.

Title: Re: Sneaky Sequences
Post by TenaliRaman on Aug 5^th, 2003, 3:03am

so the integer sequence result is wrong???

so we need to think of some other teknik???
(i will be recommending "teknik" to oxford and other dictionaries, it seems to sound correct and its short too ;D ok this comment was not reqd here)

i still stand by my reason to #4 i don't care what you are thinking Sir Col :D

However i am still trying to decode leonid here for 2 and 3.

Title: Re: Sneaky Sequences
Post by Sameer on Aug 5^th, 2003, 7:09am

ok figured out the second one... it just got visible when i wrote it down on the paper ;D
Can somebody hint me for the third one??

[hide]
alright the commas dont matter ... write down square of each number and separate them by two digits using commas... so

1 4 9 16 25 36 .. and so on.. separating gives..

14, 91, 62 .. etc...

since the square of 8 is mentioned last and first digits of 9 square the "unseparated" sequence goes like this

... 64 81 100 121 144

separating out with commas gives [/hide]

.. , 48, 11, 00, 12, 11, 44 ...

Title: Re: Sneaky Sequences
Post by Sameer on Aug 20^th, 2003, 11:59am

I wouldn't mind a quick hint on #3 and #4. it's been eating my brain plssssssssss....

Ok a quick sneaky sequence for the road...

2, 6, 12, 17, 20, 21, 22, ?

Title: Re: Sneaky Sequences
Post by Sir Col on Aug 20^th, 2003, 4:34pm

As they've been going for quite a while now, here are some hints:

3. Think about the a particular property that all of the listed numbers have in common.

4. Although more famous for the "beginning and the end," it's the ending that will be of most help. ;)

Quote:

2, 6, 12, 17, 20, 21, 22, ...

No ideas! Hmm... is it mathematical?

Title: Re: Sneaky Sequences
Post by Sameer on Aug 21^st, 2003, 7:27am

Yup Nothing but mathematical!!! Inspired from "one of the answers" to "one of the questions" you posted here. 8)

Title: Re: Sneaky Sequences
Post by Sandy Fernando on Aug 26^th, 2003, 11:33pm

Sequence 4:
[hide]
Consider the Greek Alphabet: alphA, betA, gammA, deltA, epliloN, zetA, etA, thetA, iotA, kappA, lambdA
[/hide]

Title: Re: Sneaky Sequences
Post by Sir Col on Aug 27^th, 2003, 1:52am

Very good, Sandy! 8)

Title: Re: Sneaky Sequences
Post by Sameer on Aug 27^th, 2003, 6:56am

oh that was awesome.. i am still dumbfounded on 3rd ???

Title: Re: Sneaky Sequences
Post by Sir Col on Aug 27^th, 2003, 8:17am

Hint for #3: <[hide]It is not strictly mathematical. In fact, it's not so much how you say them, rather how you would...[/hide]> ;)

Any hints for your sequence, Sameer?

Title: Re: Sneaky Sequences
Post by Sameer on Aug 27^th, 2003, 8:29am

I will point out to TenaliRaman's and Icarus's answer to #3 problem of urs ;D

Title: Re: Sneaky Sequences
Post by Sir Col on Aug 27^th, 2003, 9:29am

Okay, 2, 6, 12, 17, 20, 21, 22, ..., will produce the binary string, 1011101111101111011000...

It is then possible to split it as, 10, 11, 101, 111, 1011, 1101, ... which is the primes, 2, 3, 5, 7, 11, 13, ...

The last block (not used) is 1000, and as the next prime is 17, we would like the block 10001. As we require the presence of a zero the find the next term, we must include 19 too: 10011. This will create the string: 1011101111101111011000110011...

So the sequence will be 2, 6, 12, 17, 20, 21, 22, 25, 26, ...

Very clever, Sameer. 8)

Title: Re: Sneaky Sequences
Post by wowbagger on Aug 27^th, 2003, 10:29am

on 08/27/03 at 09:29:21, Sir Col wrote:

Okay, 2, 6, 12, 17, 20, 21, 22, ..., will produce the binary string, 1011101111101111011000...

Ok, I've looked at the numbers for a while now and can't see how you arrive at your binary string.


base 10  base 2
   2         10
   6        110
  12       1100
  17      10001
  20      10100
  21      10101
  22      10110

What produces your string?

Title: Re: Sneaky Sequences
Post by Sir Col on Aug 27^th, 2003, 11:31am

Sorry, I should have explained, but I was following on from Sameer's subtle hint, without thinking of explaining, that it was related to an idea that TenaliRaman had for sequence 3 originally.

Basically, we produce a string of 1's, and place a zero at positions determined by the sequence: 2, 6, 12, 17, 20, ...
11111111111111111111
10111011111011110110

That is, 2nd, 6th, 12th, 17th, 20th, ... positions.

The original idea came about from the sequence generated in the same way with Fibonacci numbers (missing the 1st term). So 1, 2, 3, 5, 8, 13, ... are converted to binary (1, 10, 11, 101, 1000, 1011, ... ) and juxtaposed to form a continuous binary string: 1101110110001011...

The sequence is then made by reading of the positions of the zeroes: 3, 7, 10, 11, 12, ...

What Sameer had done, to create his sequence, is the same thing with primes. All I had to do was reverse his method by first forming the string and then finding possible points to break the string up, so that the resulting sequence would be familiar.

Title: Re: Sneaky Sequences
Post by wowbagger on Aug 27^th, 2003, 12:35pm

on 08/27/03 at 11:31:42, Sir Col wrote:

I was following on from Sameer's subtle hint, without thinking of explaining, that it was related to an idea that TenaliRaman had for sequence 3 originally.

Thanks for explaining. Obviously, I didn't make that connection. Maybe I should have just stared a little longer on those many 1's...

Title: Re: Sneaky Sequences
Post by Sameer on Aug 27^th, 2003, 1:00pm

You nailed it ;D 8)

Title: Re: Sneaky Sequences
Post by Sameer on Aug 27^th, 2003, 1:31pm

3>
:: [hide]
Does this sequence by any chance have a correlation with vowels in english???

If yes then the remaining sequence would be

17,20,23,27 ...

[/hide]

Btw I just notice I am a junior member woohoo 8)

Title: Re: Sneaky Sequences
Post by Sir Col on Aug 27^th, 2003, 4:56pm

Yes, well done, and well done, in that order. ;)