wu :: forums « wu :: forums - Sneaky Sequences » Welcome, Guest. Please Login or Register. Feb 10th, 2016, 12:40am RIDDLES SITE WRITE MATH! Home Help Search Members Login Register
 wu :: forums    riddles    easy (Moderators: william wu, Eigenray, Grimbal, SMQ, towr, Icarus, ThudnBlunder)    Sneaky Sequences « Previous topic | Next topic »
 Pages: 1 2 Reply Notify of replies Send Topic Print
 Author Topic: Sneaky Sequences  (Read 3280 times)
Sir Col
Uberpuzzler

impudens simia et macrologus profundus fabulae

Gender:
Posts: 1825
 Sneaky Sequences   « on: Jun 3rd, 2003, 10:09am » Quote Modify

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!)
 IP Logged

mathschallenge.net / projecteuler.net
TenaliRaman
Uberpuzzler

I am no special. I am only passionately curious.

Gender:
Posts: 999
 Re: Sneaky Sequences   « Reply #1 on: Jun 3rd, 2003, 11:10am » Quote Modify

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

 IP Logged

Self discovery comes when a man measures himself against an obstacle - Antoine de Saint Exupery
Sir Col
Uberpuzzler

impudens simia et macrologus profundus fabulae

Gender:
Posts: 1825
 Re: Sneaky Sequences   « Reply #2 on: Jun 3rd, 2003, 11:59am » Quote Modify

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

mathschallenge.net / projecteuler.net
Leo Broukhis
Senior Riddler

Gender:
Posts: 459
 Re: Sneaky Sequences   « Reply #3 on: Jun 3rd, 2003, 2:25pm » Quote Modify

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!
 IP Logged
Sir Col
Uberpuzzler

impudens simia et macrologus profundus fabulae

Gender:
Posts: 1825
 Re: Sneaky Sequences   « Reply #4 on: Jun 3rd, 2003, 3:29pm » Quote Modify

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.

 IP Logged

mathschallenge.net / projecteuler.net
TenaliRaman
Uberpuzzler

I am no special. I am only passionately curious.

Gender:
Posts: 999
 Re: Sneaky Sequences   « Reply #5 on: Jun 4th, 2003, 8:13am » Quote Modify

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
 « Last Edit: Jun 4th, 2003, 8:19am by TenaliRaman » IP Logged

Self discovery comes when a man measures himself against an obstacle - Antoine de Saint Exupery
Sameer
Uberpuzzler

Pie = pi * e

Gender:
Posts: 1258
 Re: Sneaky Sequences   « Reply #6 on: Aug 4th, 2003, 3:10pm » Quote Modify

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..
 IP Logged

"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
Sameer
Uberpuzzler

Pie = pi * e

Gender:
Posts: 1258
 Re: Sneaky Sequences   « Reply #7 on: Aug 4th, 2003, 3:19pm » Quote Modify

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
 « Last Edit: Aug 4th, 2003, 3:22pm by Sameer » IP Logged

"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
Sir Col
Uberpuzzler

impudens simia et macrologus profundus fabulae

Gender:
Posts: 1825
 Re: Sneaky Sequences   « Reply #8 on: Aug 4th, 2003, 4:36pm » Quote Modify

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.
 IP Logged

mathschallenge.net / projecteuler.net
Icarus
wu::riddles Moderator
Uberpuzzler

Boldly going where even angels fear to tread.

Gender:
Posts: 4863
 Re: Sneaky Sequences   « Reply #9 on: Aug 4th, 2003, 5:21pm » Quote Modify

on Jun 4th, 2003, 8:13am, TenaliRaman wrote:
 For #3,i did a bit of cheat. i checked the online ....Integer Sequence

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.
 IP Logged

"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
Sir Col
Uberpuzzler

impudens simia et macrologus profundus fabulae

Gender:
Posts: 1825
 Re: Sneaky Sequences   « Reply #10 on: Aug 4th, 2003, 6:28pm » Quote Modify

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

mathschallenge.net / projecteuler.net
TenaliRaman
Uberpuzzler

I am no special. I am only passionately curious.

Gender:
Posts: 999
 Re: Sneaky Sequences   « Reply #11 on: Aug 5th, 2003, 3:03am » Quote Modify

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.
 IP Logged

Self discovery comes when a man measures himself against an obstacle - Antoine de Saint Exupery
Sameer
Uberpuzzler

Pie = pi * e

Gender:
Posts: 1258
 Re: Sneaky Sequences   « Reply #12 on: Aug 5th, 2003, 7:09am » Quote Modify

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 ...
 « Last Edit: Aug 5th, 2003, 11:47am by Sameer » IP Logged

"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
Sameer
Uberpuzzler

Pie = pi * e

Gender:
Posts: 1258
 Re: Sneaky Sequences   « Reply #13 on: Aug 20th, 2003, 11:59am » Quote Modify

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, ?
 IP Logged

"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
Sir Col
Uberpuzzler

impudens simia et macrologus profundus fabulae

Gender:
Posts: 1825
 Re: Sneaky Sequences   « Reply #14 on: Aug 20th, 2003, 4:34pm » Quote Modify

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?
 IP Logged

mathschallenge.net / projecteuler.net
Sameer
Uberpuzzler

Pie = pi * e

Gender:
Posts: 1258
 Re: Sneaky Sequences   « Reply #15 on: Aug 21st, 2003, 7:27am » Quote Modify

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

"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
Sandy
Newbie

Gender:
Posts: 1
 Re: Sneaky Sequences   « Reply #16 on: Aug 26th, 2003, 11:33pm » Quote Modify

Sequence 4:

Consider the Greek Alphabet: alphA, betA, gammA, deltA, epliloN, zetA, etA, thetA, iotA, kappA, lambdA
 « Last Edit: Aug 26th, 2003, 11:41pm by Sandy » IP Logged
Sir Col
Uberpuzzler

impudens simia et macrologus profundus fabulae

Gender:
Posts: 1825
 Re: Sneaky Sequences   « Reply #17 on: Aug 27th, 2003, 1:52am » Quote Modify

Very good, Sandy!
 IP Logged

mathschallenge.net / projecteuler.net
Sameer
Uberpuzzler

Pie = pi * e

Gender:
Posts: 1258
 Re: Sneaky Sequences   « Reply #18 on: Aug 27th, 2003, 6:56am » Quote Modify

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

"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
Sir Col
Uberpuzzler

impudens simia et macrologus profundus fabulae

Gender:
Posts: 1825
 Re: Sneaky Sequences   « Reply #19 on: Aug 27th, 2003, 8:17am » Quote Modify

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?
 IP Logged

mathschallenge.net / projecteuler.net
Sameer
Uberpuzzler

Pie = pi * e

Gender:
Posts: 1258
 Re: Sneaky Sequences   « Reply #20 on: Aug 27th, 2003, 8:29am » Quote Modify

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

"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
Sir Col
Uberpuzzler

impudens simia et macrologus profundus fabulae

Gender:
Posts: 1825
 Re: Sneaky Sequences   « Reply #21 on: Aug 27th, 2003, 9:29am » Quote Modify

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.
 « Last Edit: Aug 27th, 2003, 9:30am by Sir Col » IP Logged

mathschallenge.net / projecteuler.net
wowbagger
Uberpuzzler

Gender:
Posts: 727
 Re: Sneaky Sequences   « Reply #22 on: Aug 27th, 2003, 10:29am » Quote Modify

on Aug 27th, 2003, 9:29am, 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`

 IP Logged

Sir Col
Uberpuzzler

impudens simia et macrologus profundus fabulae

Gender:
Posts: 1825
 Re: Sneaky Sequences   « Reply #23 on: Aug 27th, 2003, 11:31am » Quote Modify

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.
 « Last Edit: Aug 27th, 2003, 11:34am by Sir Col » IP Logged

mathschallenge.net / projecteuler.net
wowbagger
Uberpuzzler

Gender:
Posts: 727
 Re: Sneaky Sequences   « Reply #24 on: Aug 27th, 2003, 12:35pm » Quote Modify

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.

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