more puzzles 2
Michael k Notch
Hre is another set of fun puzzles:
Here are some puzzles for you to work on:
1. H I J K L M N O
The letters above represent a common household substance. What is it?
2. A B C D E F G
H I J K M N O
P Q R S T U V
W X Y Z
Heres an idea for a greeting card puzzle.
On what holiday would you send the above alphabet?
3. _ 10 11 21 31 401
Find the first number of the series.
4. P R N D _ _
What are the next two entries in this sequence?
Michael k Notch no...@SRC.Honeywell.COM
Honeywell S&RC/SIP/MSP MN65-2300
3660 Technology Drive
Minneapolis, Mn 55413 (612) 782-7594
Brian V. Smith
<
< 4. P R N D _ _
<
<
< What are the next two entries in this sequence?
<
<
< Michael k Notch no...@SRC.Honeywell.COM
< Honeywell S&RC/SIP/MSP MN65-2300
< 3660 Technology Drive
< Minneapolis, Mn 55413 (612) 782-7594
\/
\/
\/
L2 L1
(more)
\/
\/
The gear indicator on a 3-speed automatic.
_____________________________________
Brian V. Smith (bvs...@lbl.gov)
Lawrence Berkeley Laboratory
We don't need no signatures!
L2 L1
Gary Piatt
=> Here are some puzzles for you to work on:
These puzzles are much too easy. Got any that are harder?
Spoilers ahead:
=>1. H I J K L M N O
=> The letters above represent a common household substance. What is it?
water (H to O == H2O)
=>2. A B C D E F G
=> H I J K M N O
=> P Q R S T U V
=> W X Y Z
=> Heres an idea for a greeting card puzzle.
=> On what holiday would you send the above alphabet?
Christmas (no "L" == NOEL)
=>3. _ 10 11 21 31 401
=>
=> Find the first number of the series.
=>
If the last number in this sequence were "41", then the first number
would probably be "1". As the problem stands, it looks like several
puzzles combined. Someone else will have to solve this one.
=>4. P R N D _ _
=> What are the next two entries in this sequence?
Either "L 2" or "1 2" or "L1 L2", depending on the kind of car you drive.
-------------------------------------------------------------------------------
Hstu R/ {osyy Vs,ntofhr. <sdd/ hstodpm#[tod,/y,v/vp,
-------------------------------------------------------------------------------
Ranjan Samuel Muttiah
>These puzzles are much too easy. Got any that are harder?
Sure.
(x - a)(x - b) = x**2 - x(a + b) + ab
(x - a)(x - b)(x - c) = (x - c)[x**2 - x(a + b) + ab]
:
:
(x - a)(x - b) ........... (x - z ) = ?? :-)
Paul R. Chernoff
>
>=>
>=> Find the first number of the series.
>=>
>
>If the last number in this sequence were "41", then the first number
>would probably be "1". As the problem stands, it looks like several
>puzzles combined. Someone else will have to solve this one.
>
----------------
A group of about half a dozen of us were unable to get anywhere with this;
but we assume that `401' is correct, and that the solution depends on
some kind of joke or verbal trick like the other three. Seems that this
one is hard enough.
===============
Some additional puzzles :
(1). Find the next few terms in the following sequence:
E Z D V F S S _ _ _
(2). Using only the four arithmetic operations +, -, *, /,
make 24 from 3,3,7,7.
(For example, 7*3 + 3 = 24, but this is not a solution because
one of the 7's is left over.) There is no restriction on the
number of times a given OPERATION can be used, and no requirement
that they all be used.
(3). The following represents a common phrase:
1,000,000 ENTURIES
=================================
# Paul R. Chernoff cher...@math.berkeley.edu #
# Department of Mathematics ucbvax!math!chernoff #
# University of California chernoff%ma...@ucbvax.bitnet #
# Berkeley, CA 94720 #
Mark Nelson
>===============
>Some additional puzzles :
>
>(1). Find the next few terms in the following sequence:
>
> E Z D V F S S _ _ _
>
O N Z
first letters of 1, 2, 3, ... in German:
Eine, Zwei, Drei, ..., Ocht, Neun, Zehn
I'm sure I've managed to misspell at least one of these.
Mark Nelson ...!rutgers!udel!nelson or nel...@udel.edu
This function is occasionally useful as an argument to other functions
that require functions as arguments. -- Guy Steele
Herb Kunze
(x - a)(x - b) ......(x - x)(x - y)(x - z) = 0 !
^^^^^^^
Herb...
*-------------------------------*----------------------------------------------*
* Herb Kunze * 'If Jiminy Cricket were here, *
* Applied Math Department * I'd skoosh him.' *
* University of Waterloo * - Calvin from Calvin & Hobbes *
* hek...@trillium.waterloo.edu * *
*-------------------------------*----------------------------------------------*
Dan Tilque;6291545;92-101;OPUS_SW;
Paul R. Chernoff writes:
>
>(1). Find the next few terms in the following sequence:
>
> E Z D V F S S _ _ _
A N Z
We forbade this one in English, shall we outlaw it in other languages
too?
---
Dan Tilque -- da...@twaddl.LA.TEK.COM
Erik Talvola
Sure.
Not that much harder.
(x - a)(x - b) ...... (x - x)(x - y)(x - z) = 0
Sorry, I don't have any good puzzles on me right now...
--
+----------------------------+
! Erik Talvola | "It's just what we need... a colossal negative
! tal...@janus.berkeley.edu | space wedgie of great power coming right at us
! ...!ucbvax!janus!talvola | at warp speed." -- Star Drek
Joe Keane
J. Matsko) writes:
>What comes next?
>
>100 200 300 301 302 303 304 ?
800?
Vincent J. Matsko
303, 304, ?
No, Joe, it's not 800. The trick that worked in Michael Notch's series,
although applicable, does not yield a correct answer.
For those who would like a hint, I'll post a message with the heading
``HINT!!!''
-Vince
Gary Piatt
...spoiler, hell! It's the *answer*!
Paul R. Chernoff writes:
=>(3). The following represents a common phrase:
=>
=> 1,000,000 ENTURIES
CUTE! "Long time, no see"
-Garison-
...here's another puzzle; let me know when you figure it out.
Paul R. Chernoff
>Arrrrrrghhhhhhh. Keep these out of sci.math, please. There is
>no mathematical content in any of these problems.
I must agree, and I do apologize for the trivial content
of my previous posting in this category.
Here's a less trivial "fill in the blanks" brain teaser:
1,2,3,.......,aleph_0,..., _?_ , 2^{\aleph_0}, _?_ ,.....
Have fun!
Tim Bedding
>
> ok then. Give me an odd perfect number.
Ain't no such thing. There's a one-to-one correspondence between perfect
numbers (whixh are the sum of their factors, including 1) and Mersenne
primes (2^n - ):
Given 2^n - 1 is prime, then the corresponding perfect number is
(2^n - 1) * 2^(n-1).
Not likely to be odd (unless you define 1 as perfect, which people don't).
Tim Bedding
School of Physics, Uni of Sydney
Bernie Cosell
}From article <75...@medusa.cs.purdue.edu>, by mut...@cs.purdue.EDU (Ranjan Samuel Muttiah):
}>
}> ok then. Give me an odd perfect number.
}
}Ain't no such thing. There's a one-to-one correspondence between perfect
}numbers (whixh are the sum of their factors, including 1) and Mersenne
}primes (2^n - ):
Not true -- go review the proof and you'll see that it was an *assumption* of
the proof that it was an even perfect number, and in that realm you're right:
a number is an *even* perfect number iff .... but last I heard the problem
was still open as to whether there was an odd perfect number or not.
/Bernie\
S. Y. Cheung
>I received some replies regarding my series 100, 200, 300, 301, 302,
>303, 304, ?
>
>No, Joe, it's not 800. The trick that worked in Michael Notch's series,
>although applicable, does not yield a correct answer.
>
Maybe 404.
--
Shun Yan Cheung
Georgia Insitute of Technology, Atlanta Georgia, 30332
...!{akgua,allegra,amd,hplabs,ihnp4,seismo,ut-ngp}!gatech!gitpyr!cheung
Michael Jones
>These puzzles are much too easy. Got any that are harder?
I accept the challenge!
Two, yes Two! postings in one. Actually a statement along
with a "new" puzzle (in response to the request for "a puzzle
of greater difficulty").
The Statement:
I really like number sequence puzzles which are actually
mathematical in nature. I *really* dislike puzzles which have
answers of the form:
"Obviously 17 and 42, the number of letters in the names
of prime numbered months when spelled in Serbo-Croatian"
There should be a disclaimer associated with non-mathematical
mathematically-phrased puzzles! (This would include all those
"street numbers where (subway|bus|train|...) stops in city x"
puzzles too).
The Puzzle:
The numbers in the following list are related and in order
(that is they are P(n), P(n+1), ... for some property or other
mathematical relation P). What are the next few numbers which
posess this property ?
44708635679
49388550606
82693916578
94204591914
28116440335967
4338281769391370
-- Michael T. Jones Email: ...!mcnc!rti!stdc01!mjones --
-- The wise man will pursue Paper: 3101-H Aileen Drive, Raleigh NC 27606 --
-- excellence in all things Voice: W:(919)361-3800 and H:(919)851-7979 --
--
-- Michael T. Jones Email: ...!mcnc!rti!stdc01!mjones --
-- The wise man will pursue Paper: 3101-H Aileen Drive, Raleigh NC 27606 --
-- excellence in all things Voice: W:(919)361-3800 and H:(919)851-7979 --
Michael Jones
>>In article <29...@mirror.UUCP> gar...@prism.TMC.COM (Gary E. Piatt) writes:
>>These puzzles are much too easy. Got any that are harder?
(x - a)(x - b) ... (x - x) ... (x - z) = 0, since (x - x) = 0
Is there more than this? Was this a rhetorical puzzle, not intended
to be answered?
Tim Eakin
>
> I really like number sequence puzzles which are actually
>mathematical in nature.
>(that is they are P(n), P(n+1), ... for some property or other
>mathematical relation P). What are the next few numbers which
>posess this property ?
OK then, how about this one :
2 3 7 43 13 53 5 -?-
If this is too hard or too easy, here are some hints to make it easier
and a variation to make it harder :
2 3 7 43 13 53 5 -?-
Hints: All numbers in the sequence are decimal (base 10).
All numbers in the sequence are prime.
All numbers in the sequence are unique.
There is no terminal number in the sequence.
Harder question (which is also a hint) :
Is every prime number present in the infinite sequence ?
If not, what is the smallest prime that isn't ?
*warning* -- I don't know the answer to this question.
I don't know if anyone knows the answer.
It is here primarily as a hint,
so spend time on it at your own risk.
Ranjan Samuel Muttiah
>In article <75...@medusa.cs.purdue.edu> mut...@cs.purdue.EDU (Ranjan Samuel Muttiah) writes:
>
> >These puzzles are much too easy. Got any that are harder?
>
> Sure.
>
>
>Not that much harder.
ok then. Give me an odd perfect number.
Thomas O Andrews
no mathematical content in any of these problems.
If you must flame me for this, do it my E-mail.
Thomas O Andrews
tho...@athena.mit.edu
David Klur
>
> The letters above represent a common household substance. What is it?
>
>2. A B C D E F G
> H I J K M N O
> P Q R S T U V
> W X Y Z
>
> Heres an idea for a greeting card puzzle.
> On what holiday would you send the above alphabet?
>
>4. P R N D _ _
>
> What are the next two entries in this sequence?
L1 and L2 (gears in a car)
_
| \ __ . _|
|_/ (_|~\/|(_)`
David Klur
klur@eniac
(215) 386-4412
(215) FUNGI-12
Vincent J. Matsko
What comes next?
100 200 300 301 302 303 304 ?
-Vince
Niall Graham
2 3 7 43 13 53 5 .....
.
.
.
.
.
.
.
.
.
.
.
.
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The next number is 6221671
solution follows
.
.
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Take the product of all the previous terms and add 1.
Then select the smallest divisor of the result.
In this case the product +1 is a prime, dammit :-)
Niall Graham
Computing Research Laboratory
New Mexico State University
Las Cruces, NM 88003
--
Niall Graham ni...@nmsu.edu
Computing Research Lab.
New Mexico State University "I aint down here for your love or money
Las Cruces, NM 88001 I'm down here for your soul"
Nick Cave
Fred LaMaster
> =>
> => Find the first number of the series.
> =>
>
> If the last number in this sequence were "41", then the first number
> would probably be "1". As the problem stands, it looks like several
> puzzles combined. Someone else will have to solve this one.
How about "0". (Sum the digits in each number).
--
Fred LaMaster fpl%hpf...@hplabs.hp.com or ...!hplabs!hpfidlf!fpl
Graeme Hiebert
Why, 0, of course [ ... (x - v)(x - w)(x - x)(x - y)(x - z) ]
^^^^^^^
Now, can you give a numerical solution to
sin x/n
The answer is independent of x and n, where n<>0.
-g
--
Graeme E. Hiebert | So many of us seek pleasures to acquire
| happiness; and yet, so few of us are
hie...@mdivax1.uucp | happy with the pleasures we've found.
...!ubc-cs!van-bc!mdivax1!hiebert |
Paul Hudson
[Old & pointless, but here you are]
Now, can you give a numerical solution to
sin x/n
The answer is independent of x and n, where n<>0.
Canceling n top & bottom.
six.
--
Paul Hudson These opinions void where prohibited by law.
Until 23 August (but (e)mail will be forwarded for a while)
MAIL: Monotype ADG, Science Park, Cambridge, CB4 4FQ, UK.
PHONE: +44 (223) 420018 EMAIL: pa...@moncam.co.uk,
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On vacation until September 6, then
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PHONE: 39 + 2 + 445701 FAX: 39 + 2 + 4454225
Frobozz
>
> The numbers in the following list are related and in order
>(that is they are P(n), P(n+1), ... for some property or other
>mathematical relation P). What are the next few numbers which
>posess this property ?
>
> 44708635679
> 49388550606
> 82693916578
> 94204591914
> 28116440335967
> 4338281769391370
>
This is quite simple, using LaGrange Interpolation I find that:
n P(n)
-----------------------
1 44708635679
2 49388550606
3 82693916578
4 94204591914
5 28116440335967
6 4338281769391370
7 25608839317066282
8 89140171874316634
9 237052812806328375
the bc script to give the above results is below (I didn't even try to simplify
the resulting polynomial --- I left my HP-28 at home today ;-)
----------------------------8<----------------------
define p(x) {
auto a,b,c,d,e,f,r
a= (x-2)*(x-3)*(x-4)*(x-5)*(x-6)/(-120);
b=(x-1) *(x-3)*(x-4)*(x-5)*(x-6)/24;
c=(x-1)*(x-2) *(x-4)*(x-5)*(x-6)/(-12);
d=(x-1)*(x-2)*(x-3) *(x-5)*(x-6)/12;
e=(x-1)*(x-2)*(x-3)*(x-4) *(x-6)/(-24);
f=(x-1)*(x-2)*(x-3)*(x-4)*(x-5) /120;
r= 44708635679*a;
r+= 49388550606*b;
r+= 82693916578*c;
r+= 94204591914*d;
r+= 28116440335967*e;
r+=4338281769391370*f;
return(r)
}
p(1)
p(2)
p(3)
p(4)
p(5)
p(6)
p(7)
p(8)
p(9)
----------------------------8<----------------------
just run bc < the above file and the result appears.
[ if you don't have bc then tough luck :-]
ok, so I know that nothing subtle was done, but it does satisfy the question.
Paul
seeya
SNIF
--