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Sir Col
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Sneaky Sequences
« on: Jun 3rd, 2003, 10:09am » |
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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!)
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TenaliRaman
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Re: Sneaky Sequences
« Reply #1 on: Jun 3rd, 2003, 11:10am » |
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4>
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
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Sir Col
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Re: Sneaky Sequences
« Reply #2 on: Jun 3rd, 2003, 11:59am » |
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Incredibly, you got the right answer for #4, TenaliRaman, but for completely the wrong reason! 
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Leo Broukhis
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Re: Sneaky Sequences
« Reply #3 on: Jun 3rd, 2003, 2:25pm » |
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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> 11 Who cares about punctuation?
3> 17 E-e-e haw!
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Sir Col
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Re: Sneaky Sequences
« Reply #4 on: Jun 3rd, 2003, 3:29pm » |
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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.
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TenaliRaman
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Re: Sneaky Sequences
« Reply #5 on: Jun 4th, 2003, 8:13am » |
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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 ....Integer Sequence
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| « Last Edit: Jun 4th, 2003, 8:19am by TenaliRaman » |
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Sameer
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Re: Sneaky Sequences
« Reply #6 on: Aug 4th, 2003, 3:10pm » |
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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..
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Sameer
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Re: Sneaky Sequences
« Reply #7 on: Aug 4th, 2003, 3:19pm » |
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Ok I figured out the first one... hope i am write
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
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| « Last Edit: Aug 4th, 2003, 3:22pm by Sameer » |
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"Obvious" is the most dangerous word in mathematics.
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Proof is an idol before which the mathematician tortures himself.
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Sir Col
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Re: Sneaky Sequences
« Reply #8 on: Aug 4th, 2003, 4:36pm » |
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That's the ticket for #1, Sameer; and, of course, you're right about the last two.
That just leaves #4. The answer is ::N::, 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.
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Icarus
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Re: Sneaky Sequences
« Reply #9 on: Aug 4th, 2003, 5:21pm » |
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on Jun 4th, 2003, 8:13am, TenaliRaman wrote:
I tried that, but the answer it gives for 3, 7, 10, 11, 12 is "the location of the nth 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.
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Sir Col
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Re: Sneaky Sequences
« Reply #10 on: Aug 4th, 2003, 6:28pm » |
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Ah, I never thought of checking the database. Leonid's answer is correct and, as always, his clues are very subtle.
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TenaliRaman
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Re: Sneaky Sequences
« Reply #11 on: Aug 5th, 2003, 3:03am » |
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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 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 
However i am still trying to decode leonid here for 2 and 3.
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Sameer
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Re: Sneaky Sequences
« Reply #12 on: Aug 5th, 2003, 7:09am » |
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ok figured out the second one... it just got visible when i wrote it down on the paper
Can somebody hint me for the third one??
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
.. , 48, 11, 00, 12, 11, 44 ...
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| « Last Edit: Aug 5th, 2003, 11:47am by Sameer » |
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"Obvious" is the most dangerous word in mathematics.
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Proof is an idol before which the mathematician tortures himself.
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Sameer
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Re: Sneaky Sequences
« Reply #13 on: Aug 20th, 2003, 11:59am » |
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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, ?
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"Obvious" is the most dangerous word in mathematics.
--Bell, Eric Temple
Proof is an idol before which the mathematician tortures himself.
Sir Arthur Eddington, quoted in Bridges to Infinity
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Sir Col
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Re: Sneaky Sequences
« Reply #14 on: Aug 20th, 2003, 4:34pm » |
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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, ... |
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No ideas! Hmm... is it mathematical?
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Sameer
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Re: Sneaky Sequences
« Reply #15 on: Aug 21st, 2003, 7:27am » |
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Yup Nothing but mathematical!!! Inspired from "one of the answers" to "one of the questions" you posted here. 
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"Obvious" is the most dangerous word in mathematics.
--Bell, Eric Temple
Proof is an idol before which the mathematician tortures himself.
Sir Arthur Eddington, quoted in Bridges to Infinity
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Sandy
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Re: Sneaky Sequences
« Reply #16 on: Aug 26th, 2003, 11:33pm » |
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Sequence 4:
Consider the Greek Alphabet: alphA, betA, gammA, deltA, epliloN, zetA, etA, thetA, iotA, kappA, lambdA
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| « Last Edit: Aug 26th, 2003, 11:41pm by Sandy » |
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Sameer
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Re: Sneaky Sequences
« Reply #18 on: Aug 27th, 2003, 6:56am » |
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oh that was awesome.. i am still dumbfounded on 3rd
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"Obvious" is the most dangerous word in mathematics.
--Bell, Eric Temple
Proof is an idol before which the mathematician tortures himself.
Sir Arthur Eddington, quoted in Bridges to Infinity
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Sir Col
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Re: Sneaky Sequences
« Reply #19 on: Aug 27th, 2003, 8:17am » |
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Hint for #3: <It is not strictly mathematical. In fact, it's not so much how you say them, rather how you would...>
Any hints for your sequence, Sameer?
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Sameer
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Re: Sneaky Sequences
« Reply #20 on: Aug 27th, 2003, 8:29am » |
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I will point out to TenaliRaman's and Icarus's answer to #3 problem of urs
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"Obvious" is the most dangerous word in mathematics.
--Bell, Eric Temple
Proof is an idol before which the mathematician tortures himself.
Sir Arthur Eddington, quoted in Bridges to Infinity
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Sir Col
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Re: Sneaky Sequences
« Reply #21 on: Aug 27th, 2003, 9:29am » |
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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.
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| « Last Edit: Aug 27th, 2003, 9:30am by Sir Col » |
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wowbagger
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Re: Sneaky Sequences
« Reply #22 on: Aug 27th, 2003, 10:29am » |
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on Aug 27th, 2003, 9:29am, Sir Col wrote:| Okay, 2, 6, 12, 17, 20, 21, 22, ..., will produce the binary string, 1011101111101111011000... |
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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?
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Sir Col
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Re: Sneaky Sequences
« Reply #23 on: Aug 27th, 2003, 11:31am » |
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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.
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| « Last Edit: Aug 27th, 2003, 11:34am by Sir Col » |
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wowbagger
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Re: Sneaky Sequences
« Reply #24 on: Aug 27th, 2003, 12:35pm » |
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on Aug 27th, 2003, 11:31am, 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. |
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Thanks for explaining. Obviously, I didn't make that connection. Maybe I should have just stared a little longer on those many 1's...
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