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# rec.puzzles Archive (logic), part 23 of 35

( Part1 - Part2 - Part3 - Part4 - Part5 )
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Archive-name: puzzles/archive/logic/part2
Last-modified: 17 Aug 1993
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==> logic/riddle.p <==
Who makes it, has no need of it.  Who buys it, has no use for it.  Who
uses it can neither see nor feel it.

Tell me what a dozen rubber trees with thirty boughs on each might be?

As I went over London Bridge
I met my sister Jenny
I broke her neck and drank her blood
And left her standing empty

It is said among my people that some things are improved by death.
Tell me, what stinks while living, but in death, smells good?

All right.  Riddle me this:  what goes through the door without
pinching itself?  What sits on the stove without burning itself?  What
sits on the table and is not ashamed?

What work is it that the faster you work, the longer it is before
you're done, and the slower you work, the sooner you're finished?

Whilst I was engaged in sitting I spied the dead carrying the living.

I know a word of letters three.  Add two, and fewer there will be.

I give you a group of three.  One is sitting down, and will never get
up.  The second eats as much as is given to him, yet is always hungry.
The third goes away and never returns.

Whoever makes it, tells it not.  Whoever takes it, knows it not.  And
whoever knows it wants it not.

Two words, my answer is only two words.
To keep me, you must give me.

Sir, I bear a rhyme excelling
In mystic force and magic spelling
Celestial sprites elucidate
All my own striving can't relate

There is not wind enough to twirl
That one red leaf, nearest of its clan,
Which dances as often as dance it can.

Half-way up the hill, I see thee at last
Lying beneath me with thy sounds and sights --
A city in the twilight, dim and vast,
With smoking roofs, soft bells, and gleaming lights.

I am, in truth, a yellow fork
From tables in the sky
The awful cutlery.
Of mansions never quite disclosed
And never quite concealed
The apparatus of the dark
To ignorance revealed.

Many-maned scud-thumper,
Maker of worn wood,
Shrub-ruster,
Sky-mocker,
Rave!

Make me thy lyre, even as the forests are.
What if my leaves fell like its own --
The tumult of thy mighty harmonies
Will take from both a deep autumnal tone.

This darksome burn, horseback brown,
In coop and in comb the fleece of his foam
Flutes and low to the body falls home.

I've measured it from side to side,
'Tis three feet long and two feet wide.
It is of compass small, and bare
To thirsty suns and parching air.

My love, when I gaze on thy beautiful face,
Careering along, yet always in place --
The thought has often come into my mind
If I ever shall see thy glorious behind.

Then all thy feculent majesty recalls
The nauseous mustiness of forsaken bowers,
The leprous nudity of deserted halls --
The positive nastiness of sullied flowers.
And I mark the colours, yellow and black,
That fresco thy lithe, dictatorial thighs.

When young, I am sweet in the sun.
When middle-aged, I make you gay.
When old, I am valued more than ever.

I am always hungry,
I must always be fed,
The finger I lick
Will soon turn red.

All about, but cannot be seen,
Can be captured, cannot be held,
No throat, but can be heard.

I am only useful
When I am full,
Yet I am always
Full of holes.

If you break me
I do not stop working,
If you touch me
I may be snared,
If you lose me
Nothing will matter.

If a man carried my burden
He would break his back.
I am not rich,
But leave silver in my track.

Until I am measured
I am not known,
Yet how you miss me
When I have flown.

For love of me,
Easily beaten,
Never free.

When set loose
I fly away,
Never so cursed
As when I go astray.

I go around in circles
Never complain
No matter where I am led.

Lighter than what
More of me is hidden
Than is seen.

I turn around once,
What is out will not get in.
I turn around again,
What is in will not get out.

Each morning I appear
All day I will follow
No matter how fast you run,
Yet I nearly perish
In the midday sun.

Weight in my belly,
Trees on my back,
Nails in my ribs,
Feet I do lack.

Bright as diamonds,
Loud as thunder,
Never still,
A thing of wonder.

My life can be measured in hours,
I serve by being devoured.
Thin, I am quick
Fat, I am slow
Wind is my foe.

To unravel me
You need a simple key,
By locksmith's hand,
But a key that only I
Will understand.

I am seen in the water
If seen in the sky,
I am in the rainbow,
A jay's feather,
And lapis lazuli.

Glittering points
That downward thrust,
Sparkling spears
That never rust.

You heard me before,
Yet you hear me again,
Then I die,
'Till you call me again.

Three lives have I.
Gentle enough to soothe the skin,
Light enough to caress the sky,
Hard enough to crack rocks.

You can see nothing else
When you look in my face,
I will look you in the eye
And I will never lie.

Lovely and round,
I shine with pale light,
grown in the darkness,

At the sound of me, men may dream
Or stamp their feet
At the sound of me, women may laugh
Or sometimes weep

When I am filled
I can point the way,
When I am empty
Nothing moves me,
I have two skins
One without and one within.

My tines be long,
My tines be short
My tines end ere
My first report.
What am I?

With thieves I consort,
With the vilest, in short,
I'm quite at ease in depravity;
Yet all divines use me,
And savants can't lose me,
For I am the center of gravity.

As a whole, I am both safe and secure.
Behead me, and I become a place of meeting.
Restore me, and I become the domain of beasts.
What am I?

I sought my first in starry skies
Where shines the April sun;
My second came before my eyes,
And warned me to be done.

'Tis very hard to lose one's sight;
I'm blind as bat or mole;
Once hills and fields were my delight,
Now I'm no more my whole.

My first is high,
My second damp,
My whole a tie,
A writer's cramp.

A hundred and one
by fifty divide,
And if a cipher
is rightly applied,
The answer is one from nine.

What does man love more than life
Fear more than death or mortal strife
What the poor have, the rich require,
and what contented men desire,
What the miser spends and the spendthrift saves
And all men carry to their graves?

I build up castles.
I tear down mountains.
I make some men blind,
I help others to see.
What am I?

Ripped from my mother's womb,
Beaten and burned,
I become a blood-thirsty slayer
What am I?

Five hundred begins it, five hundred ends it,
Five in the middle is seen;
First of all figures, the first of all letters,
Take up their stations between.
Join all together, and then you will bring
Before you the name of an eminent king.

==> logic/riddle.s <==
Who makes it, has no need of it.  Who buys it, has no use for it.  Who
uses it can neither see nor feel it.

coffin

Tell me what a dozen rubber trees with thirty boughs on each might be?

months of the year

As I went over London Bridge
I met my sister Jenny
I broke her neck and drank her blood
And left her standing empty

gin

It is said among my people that some things are improved by death.
Tell me, what stinks while living, but in death, smells good?

pig

All right.  Riddle me this:  what goes through the door without
pinching itself?  What sits on the stove without burning itself?  What
sits on the table and is not ashamed?

the sun

What work is it that the faster you work, the longer it is before
you're done, and the slower you work, the sooner you're finished?

roasting meat on a spit

Whilst I was engaged in sitting I spied the dead carrying the living.

a ship

I know a word of letters three.  Add two, and fewer there will be.

'few'

I give you a group of three.  One is sitting down, and will never get
up.  The second eats as much as is given to him, yet is always hungry.
The third goes away and never returns.

stove, fire, and smoke

Whoever makes it, tells it not.  Whoever takes it, knows it not.  And
whoever knows it wants it not.

counterfeit money

Two words, my answer is only two words.
To keep me, you must give me.

Sir, I bear a rhyme excelling
In mystic force and magic spelling
Celestial sprites elucidate
All my own striving can't relate

Pi (digits given by length of words)

There is not wind enough to twirl
That one red leaf, nearest of its clan,
Which dances as often as dance it can.

the sun, Samuel Taylor Coleridge

Half-way up the hill, I see thee at last
Lying beneath me with thy sounds and sights --
A city in the twilight, dim and vast,
With smoking roofs, soft bells, and gleaming lights.

the past, Longfellow

I am, in truth, a yellow fork
From tables in the sky
The awful cutlery.
Of mansions never quite disclosed
And never quite concealed
The apparatus of the dark
To ignorance revealed.

lightning, Emily Dickinson

Many-maned scud-thumper,
Maker of worn wood,
Shrub-ruster,
Sky-mocker,
Rave!
Portly pusher,
Wind-slave.

the ocean, John Updike

Make me thy lyre, even as the forests are.
What if my leaves fell like its own --
The tumult of thy mighty harmonies
Will take from both a deep autumnal tone.

the west wind, Percy Bysshe Shelley

This darksome burn, horseback brown,
In coop and in comb the fleece of his foam
Flutes and low to the body falls home.

river, Gerard Manley Hopkins

I've measured it from side to side,
'Tis three feet long and two feet wide.
It is of compass small, and bare
To thirsty suns and parching air.

the grave of a child, Wordsworth

My love, when I gaze on thy beautiful face,
Careering along, yet always in place --
The thought has often come into my mind
If I ever shall see thy glorious behind.

the moon, Sir Edmund Gosse

Then all thy feculent majesty recalls
The nauseous mustiness of forsaken bowers,
The leprous nudity of deserted halls --
The positive nastiness of sullied flowers.
And I mark the colours, yellow and black,
That fresco thy lithe, dictatorial thighs.

spider, Francis Saltus Saltus

When young, I am sweet in the sun.
When middle-aged, I make you gay.
When old, I am valued more than ever.

wine

I am always hungry,
I must always be fed,
The finger I lick
Will soon turn red.

fire

All about, but cannot be seen,
Can be captured, cannot be held,
No throat, but can be heard.

wind

I am only useful
When I am full,
Yet I am always
Full of holes.

sieve (or sponge)

If you break me
I do not stop working,
If you touch me
I may be snared,
If you lose me
Nothing will matter.

heart

If a man carried my burden
He would break his back.
I am not rich,
But leave silver in my track.

snail

Until I am measured
I am not known,
Yet how you miss me
When I have flown.

time

For love of me,
Easily beaten,
Never free.

gold

When set loose
I fly away,
Never so cursed
As when I go astray.

a fart

I go around in circles
Never complain
No matter where I am led.

wagon wheel

Lighter than what
More of me is hidden
Than is seen.

iceberg

I turn around once,
What is out will not get in.
I turn around again,
What is in will not get out.

stopcock

Each morning I appear
All day I will follow
No matter how fast you run,
Yet I nearly perish
In the midday sun.

Weight in my belly,
Trees on my back,
Nails in my ribs,
Feet I do lack.

ship

Bright as diamonds,
Loud as thunder,
Never still,
A thing of wonder.

waterfall? (fireworks?)

My life can be measured in hours,
I serve by being devoured.
Thin, I am quick
Fat, I am slow
Wind is my foe.

candle

To unravel me
You need a simple key,
By locksmith's hand,
But a key that only I
Will understand.

cipher

I am seen in the water
If seen in the sky,
I am in the rainbow,
A jay's feather,
And lapis lazuli.

blue

Glittering points
That downward thrust,
Sparkling spears
That never rust.

icicle

You heard me before,
Yet you hear me again,
Then I die,
'Till you call me again.

echo

Three lives have I.
Gentle enough to soothe the skin,
Light enough to caress the sky,
Hard enough to crack rocks.

water

You can see nothing else
When you look in my face,
I will look you in the eye
And I will never lie.

Lovely and round,
I shine with pale light,
grown in the darkness,

pearl

At the sound of me, men may dream
Or stamp their feet
At the sound of me, women may laugh
Or sometimes weep

music

When I am filled
I can point the way,
When I am empty
Nothing moves me,
I have two skins
One without and one within.

glove

My tines be long,
My tines be short
My tines end ere
My first report.
What am I?

lightning

With thieves I consort,
With the vilest, in short,
I'm quite at ease in depravity;
Yet all divines use me,
And savants can't lose me,
For I am the center of gravity.

The letter 'v'.

As a whole, I am both safe and secure.
Behead me, and I become a place of meeting.
Restore me, and I become the domain of beasts.
What am I?

stable

I sought my first in starry skies
Where shines the April sun;
My second came before my eyes,
And warned me to be done.

'Tis very hard to lose one's sight;
I'm blind as bat or mole;
Once hills and fields were my delight,
Now I'm no more my whole.

?

My first is high,
My second damp,
My whole a tie,
A writer's cramp.

?

A hundred and one
by fifty divide,
And if a cipher
is rightly applied,
The answer is one from nine.

?

What does man love more than life
Fear more than death or mortal strife
What the poor have, the rich require,
and what contented men desire,
What the miser spends and the spendthrift saves
And all men carry to their graves?

nothing

I build up castles.
I tear down mountains.
I make some men blind,
I help others to see.
What am I?

sand

Ripped from my mother's womb,
Beaten and burned,
I become a blood-thirsty slayer
What am I?

?

Five hundred begins it, five hundred ends it,
Five in the middle is seen;
First of all figures, the first of all letters,
Take up their stations between.
Join all together, and then you will bring
Before you the name of an eminent king.

DAVID (Roman numerals)

==> logic/river.crossing.p <==
Three humans, one big monkey and two small monkeys are to cross a river:
a) Only humans and the big monkey can row the boat.
b) At all times, the number of human on either side of the
river must be GREATER OR EQUAL to the number of monkeys
on THAT side. ( Or else the humans will be eaten by the monkeys!)

==> logic/river.crossing.s <==
The three columns represent the left bank, the boat, and the right bank
respectively. The < or > indicates the direction of motion of the boat.

HHHMmm	.	.
HHHm	Mm>	.
HHHm	<M	m
HHH	Mm>	m
HHH	<M	mm
HM	HH>	mm
HM	<Hm	Hm
Hm	HM>	Hm
Hm	<Hm	HM
mm	HH>	HM
mm	<M	HHH
m	Mm>	HHH
m	<M	HHHm
.	Mm>	HHHm
.	.	HHHMmm

==> logic/ropes.p <==
Two fifty foot ropes are suspended from a forty foot ceiling, about
twenty feet apart.  Armed with only a knife, how much of the rope can
you steal?

==> logic/ropes.s <==
Almost all of it.  Tie the ropes together.  Climb up one of them.  Tie
a loop in it as close as possible to the ceiling.  Cut it below the
loop.  Run the rope through the loop and tie it to your waist.  Climb
the other rope (this may involve some swinging action).  Pull the rope
going through the loop tight and cut the other rope as close as
possible to the ceiling.  You will swing down on the rope through the
loop.  Lower yourself to the ground by letting out rope.  Pull the
rope through the loop.  You will have nearly all the rope.

==> logic/same.street.p <==
Sally and Sue have a strong desire to date Sam.  They all live on the
same street yet neither Sally or Sue know where Sam lives.  The houses
on this street are numbered 1 to 99.

Sally thinks she now knows the address of Sam's house and decides to
visit.

When she gets there, she finds out she is wrong.  This is not
surprising, considering Sam answered only the second question
truthfully.

Sue, unaware of Sally's conversation, asks Sam two questions.

Sue thinks she knows where Sam lives and decides to pay him a visit.
She too is mistaken as Sam once again answered only the second
question truthfully.

If I tell you that Sam's number is less than Sue's or Sally's,
and that the sum of their numbers is a perfect square multiplied
by two, you should be able to figure out where all three of them
live.

==> logic/same.street.s <==

Sally thinks she now knows the address of Sam's house and decides to
visit.

Since Sally thinks that she has enough information, I deduce
that Sam answered that his house number was a perfect square
greater than 50.  There are two of these {64,81} and Sally must
live in one of them in order to have decided she knew where Sam
lives.

When she gets there, she finds out she is wrong.  This is not
surprising, considering Sam answered only the second question
truthfully.

So Sam's house number is greater than 50, but not a perfect
square.

Sue, unaware of Sally's conversation, asks Sam two questions.

Observation: perfect cubes greater than 25 are {27, 64}, less
than 25 are {1,8}.

Sue thinks she knows where Sam lives and decides to pay him a visit.
She too is mistaken as Sam once again answered only the second
question truthfully.

Since Sam's house number is greater than 50, he told Sue that
it was greater than 25 as well.  Since Sue thought she knew
which house was his, she must live in either of {27,64}.

If I tell you that Sam's number is less than Sue's or Sally's,

Since Sam's number is greater than 50, and Sue's is even
bigger, she must live in 64.  Assuming Sue and Sally are not
roommates (although awkward social situations of this kind are
not without precedent), Sally lives in 81.

and that the sum of their numbers is a perfect square multiplied
by two, you should be able to figure out where all three of them
live.

Sue + Sally + Sam = 2 p^2        for p an integer
64  + 81    + Sam = 2 p^2

Applying the constraint 50 < Sam < 64, looks like Sam = 55 (p = 10).

In summary,
Sam = 55
Sue = 64
Sally = 81

-- Tom Smith <tom@ulysses.att.com>

==> logic/self.ref.p <==
Find a number ABCDEFGHIJ such that A is the count of how many 0's are in the
number, B is the number of 1's, and so on.

==> logic/self.ref.s <==
6210001000

For other numbers of digits:

n=1:	no sequence possible
n=2:	no sequence possible
n=3:	no sequence possible
n=4:	1210, 2020
n=5:	21200
n=6:	no sequence possible
n=7:	3211000
n=8:	42101000
n=9:	521001000
n=10:	6210001000
n>10:	(n-4), 2, 1, 0 * (n-7), 1, 0, 0, 0

No 1, 2, or 3 digit numbers are possible.  Letting x_i be the ith
digit, starting with 0, we see that (1) x_0 + ... + x_n = n+1 and
(2) 0*x_0 + ... + n*x_n = n+1, where n+1 is the number of digits.

I'll first prove that x_0 > n-3 if n>4.  Assume not, then this
implies that at least four of the x_i with i>0 are non-zero.  But
then we would have \sum_i i*x_i >= 10 by (2), impossible unless n=9,
but it isn't possible in this case (51111100000 isn't valid).

Now I'll prove that x_0 < n-1.  x_0 clearly can't equal n; assume
x_0 = n-1 ==> x_{n-1} = 1 by (2) if n>3.  Now only one of the
remaining x_i may be non-zero, and we must have that x_0 + ... + x_n
= n+1, but since x_0 + x_{n-1} = n ==> the remaining x_i = 1 ==> by
(2) that x_2 = 1.  But this can't be, since x_{n-1} = 1 ==> x_1>0.
Now assuming x_0 = n-2 we conclude that x_{n-2} = 1 by (2) if n>5
==> x_1 + ... + x_{n-3} + x_{n-1} + x_n = 2 and 1*x_1 + ... +
(n-3)*x_{n-3} + (n-1)*x_{n-1} + n*x_n = 3 ==> x_1=1 and x_2=1,

Case n>5:

We have that x_0 = n-3 and if n>=7 ==> x_{n-3}=1 ==> x_1=2 and
x_2=1 by (1) and (2).  For the case n=6 we see that x_{n-3}=2
leads to an easy contradiction, and we get the same result.  The
cases n=4,5 are easy enough to handle, and lead to the two solutions
above.
--
-- clong@romulus.rutgers.edu (Chris Long)



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