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Received: from MIT.EDU (SOUTH-STATION-ANNEX.MIT.EDU [18.72.1.2]) by bloom-picayune.MIT.EDU (8.6.13/2.3JIK) with SMTP id OAA02178; Sat, 20 Apr 1996 14:39:24 -0400 Received: from [199.164.164.1] by MIT.EDU with SMTP id AA07881; Sat, 20 Apr 96 14:12:15 EDT Received: by questrel.questrel.com (940816.SGI.8.6.9/940406.SGI) for news-answers-request@mit.edu id LAA25243; Sat, 20 Apr 1996 11:13:05 -0700 Newsgroups: rec.puzzles,news.answers,rec.answers Path: senator-bedfellow.mit.edu!bloom-beacon.mit.edu!spool.mu.edu!sdd.hp.com!swrinde!cs.utexas.edu!uunet!questrel!chris From: chris@questrel.questrel.com (Chris Cole) Subject: rec.puzzles Archive (logic), part 23 of 35 Message-Id: <puzzles/archive/logic/part2_745653851@questrel.com> Followup-To: rec.puzzles Summary: This is part of an archive of questions and answers that may be of interest to puzzle enthusiasts. Part 1 contains the index to the archive. Read the rec.puzzles FAQ for more information. Sender: chris@questrel.questrel.com (Chris Cole) Reply-To: archive-comment@questrel.questrel.com Organization: Questrel, Inc. References: <puzzles/archive/Instructions_745653851@questrel.com> Date: Wed, 18 Aug 1993 06:06:12 GMT Approved: news-answers-request@MIT.Edu Expires: Thu, 1 Sep 1994 06:04:11 GMT Lines: 929 Xref: senator-bedfellow.mit.edu rec.puzzles:25018 news.answers:11538 rec.answers:1938 Apparently-To: news-answers-request@mit.edu Archive-name: puzzles/archive/logic/part2 Last-modified: 17 Aug 1993 Version: 4 ==> 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 By inadvertent fingers dropped 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, His rollock highroad roaring down, 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. I drive men mad 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 But always straight ahead, Never complain No matter where I am led. Lighter than what I am made of, 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 To lie at your feet, 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, No key that was made 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, A lady's delight. 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. Behead me again, and I am the partner of ready. 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. your word 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 By inadvertent fingers dropped 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, His rollock highroad roaring down, 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 I drive men mad 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 But always straight ahead, Never complain No matter where I am led. wagon wheel Lighter than what I am made of, 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 To lie at your feet, All day I will follow No matter how fast you run, Yet I nearly perish In the midday sun. shadow 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, No key that was made 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. your reflection Lovely and round, I shine with pale light, grown in the darkness, A lady's delight. 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. Behead me again, and I am the partner of ready. 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 asks Sam "Is your house number a perfect square?". He answers. Then Sally asks "Is is greater than 50?". He answers again. 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 asks "Is your house number a perfect cube?". He answers. She then asks "Is it greater than 25?". He answers again. 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 asks Sam "Is your house number a perfect square?". He answers. Then Sally asks "Is is greater than 50?". He answers again. 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. Sue asks "Is your house number a perfect cube?". He answers. She then asks "Is it greater than 25?". He answers again. 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, contradiction. 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) 
