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Posts posted by bonanova

  1. You can pose this puzzle with 10 bulbs instead of with 100.

    But then it's too easy to grind it out; boring.

    You can also pose it with 1000 bulbs.

    But life is short, and people with any sense walk away, and miss the fun.

    Michlips appears to be in that [sensible <!-- s;) --><!-- s;) --> ] group.

    The whole idea is to find the short cut; and grinding it out partially can light the way.

    ergo, 100 bulbs is only moderately complex and sucks you in to the search.

    KamZhiYhi took the first step and realized bulb #1 would be on - partial credit.

    unreality went farther, saw the pattern, and found the answer.

    Here's another way to see the solution.

    Observation 1. Switches flipped an odd number of times are left ON.

    Observation 2. Switch N is flipped once for each of its factors: [1,N], etc.

    Observation 3. Factors come in pairs, but for squares one factor is repeated.

    Solution: Squares are left ON, since they have an odd number of distinct factors.

    Factors of 8: [1,8], [2,4] - Persons 1,2,4 and 8 flipped switch 8. Even number of flips. Light is OFF.

    Factors of 9: [1,9], [3,3] - Persons 1,3 and 9 flipped switch 9. Odd number of flips. Light is ON.

  2. In a room are 100 light bulbs, numbered 1 to 100.

    Outside the room are 100 switches, numbered 1 to 100. Each switch controls its same-numbered bulb.

    Initially, all the switches are off.

    100 people, numbered 1 to 100, are asked to flip some or all of the switches.

    "Flip" means "change its state" - if it's on, turn it off; if it's off, turn it on.

    Person 1 must flip every switch: 1, 2, 3, ..., 97, 98, 99, 100.

    Person 2 must flip every 2nd switch: 2, 4, 6, ..., 96, 98, 100.

    Person 3 must flip every 3rd switch: 3, 6, 9, ..., 93, 96, 99.


    Person 15 must flip every 15th switch: 15, 30, 45, 60, 75, 90.


    Person 99 must flip every 99th switch: 99.

    Person 100 must flip every 100th switch: 100.

    When each person has flipped his/her assigned switches, s/he leaves.

    Finally, you enter the room to check the bulbs.

    Assuming the 100 people did as they were instructed:

    [1] are any bulbs lit?

    [2] if not, why not?

    [3] if so, which one?

    There is an easy and a hard way to solve.

    What did person 1 do that no one else did?

    Pick a bulb. Which person flipped it?

  3. If somebody says about himself, that he lies, is it truth or lie?

    [1] It is truth. Everyone lies.

    If you recast the question as:

    If somebody says about himself, that he is lying, as he speaks, is it truth or lie?

    [2] It is a contradiction. Here's why:

    [a.] every declarative sentence, say "I am 66 years old." carries the implicit assertion

    "It is true that ... I am 66 years old." equivalently,

    "I speak the truth when I say that ... I am 66 years old.".

    [b.] To pair that assertion with the assertion "I am lying as I speak"

    transforms the statement into the contradiction

    "I speak the truth when I tell you that ... I lie as I speak."

    This need not be viewed as a paradox.

    But it is inescapably a contradiction, of the same form, for example, as the statement

    "It is raining heavily as I tell you that ... the skies are perfectly clear."

  4. A Slice implys a straight cut. the other soulutions are not 2 slices


    Maybe, maybe not.

    Onelook.com says ...

    Quick definitions (slice)

    # noun: a golf shot that curves to the right for a right-handed golfer

    # noun: a spatula for spreading paint or ink

    # noun: a thin flat piece cut off of some object -- maybe

    # noun: a share of something (Example: "A slice of the company's revenue")

    # noun: a serving that has been cut from a larger portion (Example: "A slice of bread") -- maybe

    # noun: a wound made by cutting

    # verb: hit a ball so that it causes a backspin

    # verb: cut into slices (Example: "Slice the salami, please") -- maybe

    # verb: hit a ball and put a spin on it so that it travels in a different direction

    # verb: make a clean cut through -- maybe not. This does not imply "straight."

    # name: A surname (very rare: popularity rank in the U.S.: #34695)

  5. Think about these - Back to the Paradoxes

    1. Let's say (hypothetically) there is a bullet, which can shoot through any barrier. Let's say there is also an absolutely bullet-proof armour, and nothing gets through it. What will happen, if such bullet hits such armour?

    [1] The bullet splits into two equally likely quantum states - one goes to the left, the other to the right. It re-joins behind the armor.

    [2] The armor splits into two equally likely quantum states - one just to the left of the bullet, the other just to its right. The armor re-joins after the bullet passes.

    2. Can a man drown in the fountain of eternal life?

    No. In the life hereafter we do not have to breathe.

    3. Your mission is to not accept the mission. Do you accept?

    Let me get back to you on this one. But I will say that I'm thinking about it.

    4. This girl goes into the past and kills her Grandmother. Since her Grandmother is dead the girl was never born, if she was never born she never killed her grandmother and she was born.

    [1] Since she blatantly ignored the Prime Directive, we should not even be talking about her.

    [2] I just took a drive in my own WayBack Machine and deleted this question. No reply is needed.

    5. If the temperature this morning is 0 degrees and the Weather Channel says, "it will be twice as cold tomorrow,".... What will the temperature be?

    Double Zero. C'mon, gimme a challenge.

    6. Answer truthfully (yes or no) to the following question: Will the next word you say be no?

    I'm thinking to myself that someone should go back and read #3....

    7. What happens if you are in a car going the speed of light and you turn your headlights on?

    This is soooooo easy. I'll be able to see better.

    8. I conclude with this challenge:

    Let the God Almighty create a stone, which he can not pick up (is not capable of lifting)!

    It's like the song says, that we sang as children:

    God can do anything, anything, anything,

    God can do anything but fail.

    He can save, He can keep, satisfy with joy complete,

    God can do anything, but fail.

    He's the Alpha and Omega, the beginning and the end,

    He's the fairest of ten thousand to my soul ...

    God can do anything, anything, anything.

    God can do anything but fail.

    Otherwise ... He wouldn't be Almighty.

  6. Hi UR,

    I re-read your posts, and If I understand them,

    you are saying that the equally likely cases are the numbers of reds and greens.

    5 red 0 green = same likelihood as

    4 red 1 green = same likelihood as

    3 red 2 green = same likelihood as

    2 red 3 green

    Like that defines 4 equally likely cases.

    Is that what you're saying?

    Otherwise I don't understand where we differ.



    yep! same probability... cuz there is no random distribution. I'll post this in that topic so we can continue this discussion there not here <!-- s:D --><!-- s:D -->

    Thank you, my friend -- I have seen the light.

    You've taught me well.

    If you'll excuse me I have a few things to do...

    [1] Go tell sajow4 she was right.

    A couple has two children, one of which is a girl. What is the probability the other is a girl?

    There are two possibilities, both equally likely:

    [1] 1 girl and 1 boy. Probability of the other being a girl = 0%

    [2] 2 girls and 0 boys. Probability of the other being a girl = 100%

    The probability of the other being a girl is [0% + 100%]/2 = 50%

    She'll be delighted to hear this.

    [2]Go to Morty's and flip some coins tonight.

    I'll flip a coin 10 times. What are my chances of getting all 10 tails?

    There are only 11 outcomes, all equally likely:

    [ 1] 10 tails, 0 heads - probability of winning = 100%

    [ 2] 9 tails, 1 heads - probability of winning = 0%

    [ 3] 8 tails, 2 heads - probability of winning = 0%

    [ 4] 7 tails, 3 heads - probability of winning = 0%

    [ 5] 6 tails, 4 heads - probability of winning = 0%

    [ 6] 5 tails, 5 heads - probability of winning = 0%

    [ 7] 4 tails, 6 heads - probability of winning = 0%

    [ 8] 3 tails, 7 heads - probability of winning = 0%

    [ 9] 2 tails, 8 heads - probability of winning = 0%

    [10] 1 tails, 9 heads - probability of winning = 0%

    [11] 0 tails, 10 heads - probability of winning = 0%

    Overall my chances are [100+0+0=0+0+0+0+0=0+0=0]/11 = 9.1%

    Heh heh. Some guy at Morty's said he'd give me 1024-to-1 odds.

    [3] Finally -and this is the big one - I'm going to buy a lotto ticket.

    I bought a lotto ticket. What are my chances of winning?

    There are only two possibilities, both equally likely:

    [1] it's the right number. Probability of winning = 100%

    [2] it's not the right number. Probability of winning = 0%

    Overall, my chances of winning are [100 + 0]/2 = 50%.

    This excites me, cuz I hear the lotto pays off more than $100 sometimes.

  7. The detective arrived on the scene and discovered the following:

    George was dead.

    He was found face down in the street, squashed nearly flat.

    He must have been there some time as he was cool to the touch.

    In addition, when he was found, there was a bird perched on the back of his head.

    What was George's last name?

  8. A cup of coffee next time yer in New York for anyone who can tell me what this is all about.

    Hint: reading it may put you to sleep, but it's not meant as a cure for insomnia...

    Star? Not I! Movie – it too has a star in or a cameo who wore mask – cast are livewires.

    Soda-pop straws are sold, as part-encased a hot tin, I saw it in mad dog I met. Is dog rosy? Tie-dye booths in rocks.

    All ewes lessen ill. I see sheep in Syria? He, not I, deep in Syria, has done. No one radio drew old one.

    Many moths – I fondle his; no lemons are sold. Loot delis, yob, moths in a deli bundle his tin. Pins to net a ball I won – pins burst input. I loot to get a looter a spot paler. Arm a damsel – doom a dam. Not a base camera was in a frost, first on knees on top spot. Now a camera was a widened dam.

    Ask: Cold, do we dye? No, hot – push tap, set on to hosepipe. Nuts in a pod liven.

    A chasm regrets a motto of a fine veto of wars. Too bad – I all won. A sadist sent cadets – a war reign a hero derides. A bad loser, a seer, tossed a cradle – he begat to cosset – a minaret for Carole, Beryl, Nora. We’re not as poor to self.

    I risk cold as main is tidal. As not one to delay burden, I don’t set it on “hot”. A foot made free pie race losses runnier. As draw won pull, eye won nose. Vile hero saw order it was in – even a moron saw it – no, witnessed it: Llama drops – ark riots. Evil P.M. in a sorer opus enacts all laws but worst arose. Grab a nosey llama – nil lesser good, same nicer omen.

    In pins? No, it is open. If a top spins, dip in soot.

    Madam, as I desire, dictates: Pull aside, damsels, I set a rag not for a state bastion. A test I won e.g. a contest I won.

    Kidnap, in part, an idle hero. Megastars, red, rosy, tied no tie. Blast! A hero! We do risk a yeti’s opposition!

    He too has a wee bagel still up to here held.

    Demigods pack no mask, cap nor a bonnet, for at last a case is open – I left a tip – it wets. A dog wets too. Radios to help pay my tip, pull a tip.

    Ale, zoo beer, frets yon animal. Can it? New sex arose but, we sots, not to panic – it’s ale – did I barrel? Did I lose diadem, rare carrot in a jar of mine? Droop as tops sag – unseen knots.

    A cat ate straw as buck risk cud; evil foe, nil a red nag ate? Bah! Plan it – silage. Model foot in arboreta.

    I, dark Satanist, set fire – voodoo – to slat. I design a metal as parrot, I deem it now. One vast sum is no ten in set – amen! Indeed, nine drag a yam, nine drag a tie. Dame nabs flower; can we help man? Woman is worse nob.

    Mud level rose, so refill a rut. A nag of iron I made to trot I defied – I risk leg and its ulnae. Can a pen I felt to bid dollar or recite open a crate, open a cradle, his garret?

    Sample hot Edam in a pan. I’m a rotten digger – often garden I plan, I agreed; All agreed? Aye, bore ensign; I’d a veto – I did lose us site. Wool to hem us? No, cotton. Site pen in acacias or petals a last angel bee frets in.

    I met a gorilla (simian); a mate got top snug Noel fire-lit role. Manet, Pagnol, both girdle his reed bogs.

    Flan I reviled, a vet nods to order it, Bob, and assign it. Totem users go help mates pull as eye meets eye. Son – mine – pots a free pie, yes? No. Left a tip? Order a dish to get. A ring is worn – it is gold. Log no Latin in a monsignor, wet or wise. Many a menu to note carrot.

    Cat in a boot loots; As I live, do not tell! A bare pussy, as flat on fire, I know loots guns, fires a baton, nets a hero my ale drop made too lax.

    If it is to rain, a man is a sign; I wore macs, no melons rot. I use moths if rats relive, sir, or retire.

    Vendor pays: I admire vendee, his pots net roe. Nine dames order an opal fan; I’ll ask cold log fire vendor to log igloo frost. Under Flat Six exist no devils.

    Marxist nods to Lenin. To Lenin I say: “Mama is a deb, besides a bad dosser.”

    Gen it up to get “ova” for “egg”. I recall a tarot code: yell at a dessert side-dish sale. Yes/nos a task cartel put correlate: E.S.P. rocks a man. I am a man, am no cad, I’m aware where it’s at!

    Fire! Its an ogre-god to help, man, as I go. Do not swap; draw, pull a troll!

    It’s not a cat I milk – calf, for a fee, sews a button - knit or tie damsel over us. Mined gold lode I fill until red nudes I met in a moor-top bar can. I sit, I fill a diary – trap nine men in ten-part net – oh, sir, I ask, cod nose? No, damp eel.

    So, to get a name! I say, Al! I am Al! Last, I felt, to breed, deer begat.

    To can I tie tissue – damp – or deliver Omani artist – a man of Islam.

    In a den mad dogs lived on minis a signor who lived afore targets in at. As eremites pull, I, we, surf, fantasise, mend a bad eye. No hero met satyr; Tony, as I stressed, won’t, so cosset satyr.

    A vet on isles made us sign it, a name. Foe man one sub.

    Aside no dell I fret a wallaby; metal ferrets yodel, like so. On a wall I ate rye. Bored? No, was I rapt! One more calf? O.K., calf, one more, bossy! No! Lock cabin, rob yam, sip martini. Megastar was in a risk.

    Cat? No, I’m a dog; I’m a sad loyal pet. A design I wore – kilts (a clan); if net drawn, I put it up. Royal spots snag – royal prevents rift.

    Composer, good diet, are both super, God – label it a love of art, lustre. Video bored, no wise tale e.g. a mini tale – no sagas seen. Knack: cede no foes a canal.

    Pay – as I sign I lie; clear sin it is; e.g. “Amadeus” sign I – lira for ecu, decimal – sin as liar.

    Trad artistes pull a doom, a drawer won’t.

    Is it sold loot? No, I suffered loss. A man is god; Amen! I came nice Tahiti (sic).

    It’s ale for a ban if for a fast – is role to help mash turnip? Use zoo? No - grasp order – use no zoos. Warts on time did sag.

    No grade “X” “A” Level? Oh, “A”! I’d a “B” or a “C”. So – pot? No, we lop. Date? Take no date! Bah! Play L.P.

    Miss (a lass, all right?) flew to space in NASA era. Rose no (zero) cadets ate raw. As a wise tart I fined rags red Lenin, we help pay bet – a risk – cash to Brian. I put a clam in a pool – a pool wets.

    Mahdi puts a stop to harem – miss it in one vote, lost in one, veto of none. Post-op, no tonsil; I ate; no tastier, eh? We sleep at noon time so I dare not at one; no time stops as I time tides. A bed: under it, roll; in a mania, panic!

    In a pond I did as Eros as Lee felt tenrec. “Ink” – list it under “I”. Termites put pen in a way. Democrats wonder, I too. To slay moths a dog did.

    I saw elf; elf, far now, is a devilish taboo, rag-naked. I hid a bootleg disc. I, saboteur, toss it in. Oops! No legs! Laminated, a cask, conker in it, negates all if it is simple.

    Hot pages are in a mag, nor will I peer, familiar tat, so lewd, native rot. Toner, ewe wore no trace; vagabond ewes do. Oh, Ada! Have pity! A pitiable eel – “Oh wet am I!” - to save, note: bite gill as I do.

    Call a matador minor, eh? As I live, don’t! Is torero no rigid animal debaser if tipsy? Ale drew esteem in a matador. A bolero, monks I rate play or go dig rocks; a can I step on.

    Go! Gas – it evades a bedsit – set a roost on fire. Boss sent a faded eclair to green imp or dog, I’d don a belt to boot it; if Ada hid a boot, panic.

    I mock comic in a mask, comedian is a wit if for eventide. Vole no emu loved is not a ferret, so pet or witness a weasel if not. I hired less, am not so bossy, as yet amateur.

    To stir evil, Edna can impugn a hotel: bad loos, hot on Elba: I may melt. Tart solicits it rawer, gets it rare. Push crate open; I ram buses, use no trams.

    Did I say, not to idiot nor a bare ferret, to trap rat, strap loops rat? Stewpot was on. Hot? I was red! Lessen it! Fine man on pot? No, pen inside by a bad law. So I made rips – nine delays.

    Some Roman items in a.m. ordered “Is room for a ban?” “It is,” I voted: I sat pews in aisle. Beryl, no tiro to my burden, made off for a contest, I won kiss. I may raid fine dales. I raid lochs if I to help am.

    Forecast for Clare v. Essex: If no rain, a man is ref. Fusspots net foxes.

    Senor is a gnome, latinos’ bad eyesore. Help misses run to border, Casanova, now, or drab hotel.

    Ma has a heron; I sleep, pet’s on nose, sir! Rev. I rag loved art live – fine poser. Ultra-plan: I feign, I lie: cedar to disperse – last one? No, last six. Enamel bonnet for a dark car to toss a snail at. In it all, Eve lost; Seth’s a hero slain on a trap – Rise, Sir Ogre Tamer.

    Upon Siamese box I draw design. I, knight able to help, missed an alp seen in Tangier of fine metal pots. Tin I mined rages – order nine, melt ten. Tone radios; tones are not to concur. Ten-tone radar I bomb – best fire-lit so hostel side meets eerie mini red domicile. A gulf to get is not a rare tale; no time to nod.

    Row on, evil yobs, tug, pull. If dogs drowse, fill a rut. An era’s drawers draw. Put in mid-field in a band I dig a tub deep. Staff on a remit did refill a minaret.

    Sam’s a name held in a flat, or, sir, bedsit. I wonder, is it illicit ore? No ties? A bit under? Retarded? Is ‘owt amiss? I’m on pot; not so Cecil, a posh guy a hero met. A red date was not to last so Cecil sat.

    Tip? An iota to pay, a dot; sad, I drop item. I’d ask, call, Odin, a Norseman’s god: “Pay payee we owe radio dosh o.n.o.” I to me? No, I to media.

    Peril in golf – is ball a “fore”? K.O.!

    Vexed I am re my raw desires. Alto has eye on nose but tone-muser pianist is level-eyed. I lost a tie. Blast! In uni no grades are musts. Avast! Never port! Sea may be rut.

    Part on rose? - It’s a petal. Define metal:

    Tin is … (I gulp!) can!

    I am a fine posse man, I pull a ton. Ron, a man I put on, I made suffer of evil emu’s sadism. Leo’s never a baron - a bad loss but evil – topple him, Leo’s lad. Assign a pen, can I? A pal is note decoding.

    Is damp mule tail-less? No, ill; I breed for its tone. Radio speed, to grower, grew. Open a lot? No, stamp it; if for a free peso – not ecu -deign it. Times ago stone rates, e.g. at Scilly, display a wont.

    No wish to get a design I, Sir Des, I’ve let? No bus sees Xmas fir. O.K. – cab – tart it up; tie lots – diamond, log or tinsel; first end errata edit. So “le vin (A.C.)”, Martini, Pils lager, one tonic.

    I pegged a ball up to here when I got a top star role, Beryl. Gun is too big – won’t I menace? Yes? No?

    Ill? A cold? Abet icecap’s nip. U.S.A. meets E.E.C. inside tacit sale – see! Beg a cotton tie, ma! No trial, so dodo traps exist. Arabs under-admire card label good hood stole.

    In rage erupted Etna. Will a rotunda, bare villa, to tyro. Lack car? Non-U! Get a mini! My, my, Ella, more drums per gong; get a frog – nil less. Rod, never ever sneer. Got to?

    I disperse last pair of devils (ah!) here today or else order cash to breed emus. Said I: “Are both superlative?” C.I.D. assign it lemon peel still. I wore halo of one bottle from a ref (football) – a tip; so hit last ego slap a mate got.

    Late p.m. I saw gnu here (non-a.m.) or an idea got a dog to nod – I made felt to boot.

    Fill in a lad? Nay, not all, Edna – lash to buoy. Did you biff one Venus? Not I! “Broth, girl!” ladies ordered – “No, with gin!” – a fine plate, maybe suet; no carton I made rots in it.

    Med: a hill, Etna, clears in it. Ali, Emir, to slap in/slam in. All in all I made bad losers sign it – alibi. Set a lap for a level bat.

    A bed, sir, eh? To put cat now? Drat! Such an idyll of a dog’s lair! That`s it, open it – a cage! Big nit sent rat! Some day (A.D.) send ewe. No, draw a pot now, do! Of wary rat in a six ton tub.

    Edna, ask satyr: “Tel. a.m.?” No, tel. p.m.; Israeli tuner is damp. Use item: “Anna Regina”. No! Dye main room (“salle”) red!

    Nice caps for a sea cadet in U.S.A. – Now I, space cadet, am it, sea vessel rep. Pin it on Maria, help Maria fondle her fine hotpot. No! Meet; set up to net, avoid a lesion. Set acid arena: Bruno one, Reg nil. Like it to sign in? Even I am nine-toed! I vote votes.

    Oh, can a nose-rut annoy? No, best is Dorset. I know, as liar, to snoop, malign. “I’ll order it to get a bedroom door,” began a miser I fed.

    Am I to peer, fan? Is a door by metal? Ere sun-up, drowse, nod, lose magnet. Food? Buns? I’ll ask. Corn? I’ll ask. Corn – I snack. Cats snack (cold rat). Sum for a bag: nil. First, is remit “traps in net”? Yes, on a par. Coots yell over a dam I made. Bared nudist went a foot, I made roots. I tip a canon: “Row, sir, at same tide; man one: row tug.”

    Sewer of denim axes a wide tail – a terror recipe to hero made manic. I, to resign? I ? Never!

    “oft I felt itS SENSUOUSNESS” – title fit for evening is erotic; I named a more hot epic – error retaliated – I was examined for ewe’s gut, wore no named item.

    A star is worn on a cap, it is too red. Am I too fat? Newts I’d under a bed. Am I mad? Are volleys too crap? A nosey tennis part-timer sits rifling a bar of mustard.

    Lock cans, stack cans in rocks, all in rocks, all I snub. Do often games, old ones, word-pun use; relate, my brood, as in a free pot I made fires, I manage brood. Moor debate got tired rolling, I lampoon, so trail saw on kites.

    Rod sits, ebony on nature, so Nana chose to veto video. Ten in main evening is O.T.T. i.e. killing; Ere noon, urban eradicates noise, lad, I ovate not. Put esteem on top (to hen, if reheld).

    No fair ample hair – am not I nipper-less? Eva estimated ace caps I won as united. A Caesar of space, Cinderella’s moor, Niamey Don (a Niger-an name), ties up mad sire, nut! I, Lear, simpleton male, try tasks “A” and “E”

    but not “XI”. Sanitary raw food won top award one Wednesday – a demo.

    Start nesting, I beg a cat. I? Nepotist? Ah, trials, God! A folly, Dinah, custard won’t act up; other is debatable. Velar: of palate; sibilating is “s”.

    Resold: a bed, a mill, an ill animal – snip, also trim. Eilat in Israel can tell I had ‘em. Tin I stored (am I not raconteuse?) by a metal pen. If a night, I wondered, rose, I’d all right orbit on sun, even off.

    I buoy, did you? Both Sal and Ella, Tony and Alan (“Ill if too bottle-fed, am I?”) do not. God! A toga! Ed in a Roman one, rehung! Was I, M.P. et al., to get a map? Also get salt? I, hospital lab to offer, am, or felt to be, no fool – a hero.

    Will it sleep? No, melting is sad ice. Vital re-push to be raid, I assume. Deer, both sacred roes, Leroy (a doter, eh?) has lived for. I, apt sales rep’s idiot to greens, revere vendors selling or fat egg-nog reps.

    Murder O’Malley, my mini mate – gun on rack. Calory total: liver, a bad nut or all I wanted (“et puree garnie”): lots. “Do, oh do, ogle bald racer,” I’m dared – N.U.S. bar at six.

    Esparto, dodo’s lair to name it, not to cage bees, elasticated, is nice. Esteem, as up in space, cite bad local lions, eye can emit now. G.I. boots in ugly rebel or rat’s potato gin (eh?) were hot. Pull a bad egg – epic, I note, no regal slip in it. Ram can … (I’ve lost idea!)

    Tarred nets, rifles, nitro, gold – no maid stole it. Put it, rat, back or if Sam (“X”) sees sub on televised rising, I sedate Goths. I won’t – no way.

    Alps, idyllic stage set, are not so gas-emitting, I educe. To nose, peer, far off, I tip mats onto lane. Power grew or got deep so I dare not stir. Of deer, billions sell. I ate lump – mad sign, I do cede – tonsil a pain, acne pang is sad also. Elm I help pot, live – tub’s sold; a ban or a bar, even so, elms, I’d assume, live for. Effused am I not, up in a manor, not all up in a mess.

    Open if a main A.C. plug is in it.

    Late men I fed late – pasties or not. “Rapture” by a maestro prevents a vast sum erased.

    Argon in units, albeit at solid eye level, sits in a … (I presume not) … tube, son. No eyes: a hot laser – is Ed wary?

    Mermaid, ex- evoker of all A.B.s, I flog. Nil I repaid. Emotion! Emotion, oh so do I dare, woe!

    Wee yap-yap dog’s name’s Ron. An idol lacks a dime tip, or did, as today a potato in a pitta slice costs a lot – tons. A wet adder ate more hay. Ugh! So, pal, ice cost on top? No, miss, I’m a two-sided rat, erred nut, I base it on erotic ill; It is I, red now; it is debris, rot.

    Alf, an idle he-man as “master animal lifer” did time, ran off at speed, but a G.I. did nab an idle if dim nit. Upwards rewards are natural life’s words, God. Fill up guts, boy, live now or do not emit one later. A rat on site got flu.

    Gaelic, I’m odd Erin, I’m Eire, esteemed islet. So hostile rifts ebb. Mob, I.R.A., dare not net R.U.C. – no cotton. Erase not, so I dare not nettle men in red rose garden – I’m in it.

    Stop late men if foreign at nine. Esplanades, simple hotel, bath, gin – king is Edward IX; obese; Ma is no pure mater. Go! Rise, sir; part anon.

    I also rehash tests – ‘O’ Level Latin, Italian. S.A.S., so, to track radar. Often nobleman exists alone – not sales reps – I do. Trade ceiling, i.e. final part, lures open if evil trade.

    Volga River rises on no steppe. Elsinore has a hamlet – Oh, Bard, row on Avon!

    A sacred robot nurses simple hero’s eye; dabs on it a lemon. Gas, iron, Essex often stops, suffers in a mania. Ron fixes several crofts, acer of maple. Hot, I fish; cold, I arise laden; if diary amiss, I know it set no car off. Foe-damned ruby motor, it only rebels.

    Ian I swept aside to visit, in a bar of moorside red, Romanis met in a more mossy ale den. Inspired am I, Oswald. A bay bed is nine p on top. No name, niftiness- elder saw it. Oh no! Saw top wet star’s pool – part star, part otter. Refer a baron to idiot, Tony, as I did.

    Smart ones use submarine.

    Poet, arch-super-artiste, grew artistic. I lost rattle; my amiable, not oh so old, able to hang up, mina, can deliver it, so true. “Ta, matey!” – says so Boston (Mass.) elder I hit.

    On file S.A.E. was sent – I wrote poster re fat on side, volume one – loved it, never off it, I was in. Aide mocks a manic; I mock comic, I nap: too bad I had a fit, I too. Bottle ban odd, I go drop mine, ergo trial ceded a fatness, sober if not so, or a test is debased.

    A vet is agog – no pet’s in a cask – corgi dog, royal pet, a risk no more.

    Lob a rod at a man I meet. Sewer delays pit fires – a bedlam in a dig – iron ore rots it. No devil is a hero – Nimrod.

    At a mall a cod is all I get. I bet on Eva, so Tim ate whole eel bait, I pay tip, Eva had a hood sewed. No B.A. gave car to Nero, we were not to rev it and we lost a trail; I’m a free pill, I wrong a man. I erase gap; to help miss it, I fill a set. A gent in ire knocks a cadet.

    Animals’ gel on spoon – it is so true to basics – I’d gel; too bad I hide kangaroo baths – I lived as I won raffle, flew as I did go, dash, to my, also too tired now, star comedy: A wan, inept, upset I’m retired, nut; its ilk, nicer. Nettle feels a sore; sad, I did no panic in a pain, am an ill or tired, nude, based item; it is a spot.

    Semitone, not a tone, radios emit; no, on tape; elsewhere it’s a tone.

    Tail is not on; pots open on foot, even on it, so let oven (on, it is) simmer – a hotpot’s a stupid ham stew.

    Loop a loop, animal – cat up in air.

    Both sacks I rate by apple hewn in elder’s garden if it rates, I was aware – tasted a core.

    Zones or areas, Annie, cap, so twelfth girl, lass, alas, simply (alpha beta) done, Kate. Tadpole won top Oscar, Obadiah, “O” Level axed.

    Argon gas did emit no straw, so ozone sure drops argon, oozes up in Ruth’s ample hotel or sits afar off in a bar – of elastic, is it?

    I hate cinema; cinema dogs in a mass. Older effusion to old – lost, is it now? Reward: a mood.

    All upsets it.

    Radar trails an Islamic educer of a riling issue, damages it in Israel. Ceiling is, I say, a plan, a case of one deck. Can knees sag as one Latin image elates, I wonder?

    Oboe diverts ultra foe, volatile bald ogre – push to berate; I’d do, ogre. So, p.m., Oct. first, never play organ’s stops – lay or put it up in ward ten.

    Final cast like rowing – I sedate play, old as am I, God! Am I! On tacks I ran; I saw rats. A Gemini tramp is May born.

    I back colony’s sober omen of lack of lace. Rome, not Paris, a wonder.

    Obey retail law – a noose killed oyster. Reflate my ball, a water-filled one. Disabuse no name of emanating issue.

    Damsels, I note, vary tastes so cost now desserts. I say no! Try taste more honeyed. A bad nemesis at naff ruse will upset. I, mere Satanist, e.g. rater of a devil – (Oh wrong is a sin!) – I’m no devil’s god, damned.

    Animals, if on a mat, sit. Rain, a more vile drop, made us site it in a cottage. Breed deer – bottle fits a llama.

    I lay, as I emanate, go to sleep, mad ones on docks – air is hot. Entrap, net, nine men in party raid - all if it is in a crab-pot room, an itemised, under-lit, nullified old log den – I’m sure voles made it rot in knot.

    Tubas we see far off lack limit. A cat on still or tall upward paws to no dog is an ample hot-dog, ergo nastier if tastier, eh? We, raw amid a conman, a mama in a mask, corpse et al., err.

    Octuple tracks at a son’s eyelash side distressed a tall eye doctor, a tall ace, rigger of a vote: got put in egress; odd, abased, is ebbed, as I am, Amy, asinine lot! Nine lots! Don’t six rams live? Don’t six exist?

    Alfred, nuts or fool gigolo, trod never if gold locks all in a flap on a red rose; made nine or ten stops.

    I heed never, I’m Daisy, a prod never, I terrorise viler starfish. To me suitors, no lemons, came rowing. Is a sin a mania? Rot!

    Sit! I fix a looted amp or delay more, hasten not. A baser if snug stool, wonkier, if not - Alf says - super, a ballet to no devil, is a stool too. Ban it, actor, race to no tune.

    May names I wrote wrong (Is no man in it, a long old log?) sit in row, sign irate Goths; I dare drop it. At felon’s eye I peer, fast open – I’m nosey, esteem eyes. All upset, ample hogs resume totting. Is sad nabob tired? Roots don’t evade liver in Alf’s gob.

    Deers I held right; oblong, apt enamel or tile rifle on gun spot to get a man – aim is all. I rogate, minister. Feeble gnats, alas late, prosaic, a canine pet is not to consume hot.

    Loo, wet, issues old idiot; evading, I sneer, obey a deer, gall a deer, gain alpine dragnet for egg I’d net to ram in a pan I made to help master. Rags I held, arcane poet, arcane poetic error, all odd; I bottle fine panacean lust. I’d nag elks I ride if editor toted a minor. I fog a natural life.

    Roses, or level dumb ones – rows in a mown, ample, hewn acre. Wolfsbane made it a garden in May, a garden indeed.

    Nine mates, nine tons I must save now on time – editor raps a late man. G.I.s edit also, too. Do over if tests in a task radiate. Rob ran; I, too, fled.

    “Omega” – list in alphabet.

    A gander, a line of live ducks, irk cubs. A wart, set at a cast on knee, snug as spots.

    A poor denim for a janitor, racer, armed aide, solid idler – rabid; I’d elastic in a pot, tons to sew.

    Tubes or axes went in a clam, in an oyster. Free booze – lap it all up. Pity, my apple hot, so I’d a root stew. God, a stew! Tip it at feline! Posies, a cat’s altar often, no baron packs. A monk caps dog – I meddle here – hot? Pull its leg! A bee was a hoot, eh?

    No, it is opposite. Yaks I rode wore hats, albeit on deity’s orders. Rats age more held in a trap, nip and I know it – set no cage now.

    It’s eta; no, it’s a beta – Tsar of Tonga rates isles. Mad Ed is all upset at cider, is Ed? Is a madam too? Snip? I’d snip, spot a fine position, snip nine more cinemas.

    Do ogres sell in a mall? Yes, on a barge so rats row tubs.

    Wall last canes up or Eros, an imp, lives to irk, rasp or dam all tides sent. I won’t – I was no Roman – even I saw tired row – a sore. He lives on. “No!” we yell.

    Up, now! Wards are in nurses’ sole care. I, peer, fed, am too fat? Oh, not I, test no dined ruby ale; dote not on salad it’s in – I am sad.

    Locks I rifle so troops atone re war. Only rebel or a crofter animates so cottage beheld arcades, so trees are sold, abased. I redo, rehang, I err – a wasted act; nests I’d – as an owl – laid. A boot’s raw foot, even if a foot to master, germs (ah!) can evil do.

    Pan is tune-pipe – so hot notes, paths up to honeydew.

    Odd locks, a maddened (I was aware) macaw on top, spot no seen knots, rifts or fan, I saw. Are maces a baton, madam? Oodles, madam? Rare laptops are too late – got too lit up.

    Nits rub – snip now, I’ll abate, not snip, nits I held.

    Nubile Danish tomboys I led to old loser as no melons I held; no fish to my name. Nod lower, do I dare? No, one nods a hairy snipe. (Edit: one hairy snipe, eh?) See silliness, else we’ll ask Cornish to obey deity’s or god’s item. I, God, damn it! I was in it! To Hades, acne trap, sad loser! As warts pop, a dosser I – we – vile rat, sack! Same row, oh woe! Macaroni, rats, as a hoot, tie. I vomit on rats.

  9. i thought it was a maximum of 7
    For all practical purposes.

    Here's why that makes sense.

    On your first fold, you're folding a single sheet

    On your second fold, 2 sheets

    On your third fold, 4 sheets



    On your seventh fold, it's 64 sheets.

    If you want to try for an eighth fold, it would be 128 sheets.

    Try folding pages 1-256 of a book [numbers on both sides remember].

  10. Alex wins. By a lot.

    Here's why:

    Label the aces as:

    S-ace of spades,

    H-ace of hearts,

    D-ace of diamonds,

    C-ace of clubs.

    There are 12 equally likely consecutive-ace [CA] possibilities:

    SH SD SC

    HS HD HC

    DS DH DC

    CS CH CD

    where SH means ace of spades followed by ace of hearts. etc.

    Given the [equal] probability of any of these sequences, say p[sH],

    the probability for any two consecutive aces is

    p[CA] = 12 x p[sH]

    Denoting position in the deck by 1, 2, 3, ..., 51, 52,

    p[sH] = p[1,2] + p[2,3] + ... + p[51,52]. where p[1,2] is prob of spade being card 1, heart being card 2, etc.

    The probability of a card being in a specified place in the deck is 1/52.

    The probability of a 2nd card being in a different specified place in the deck is 1/51.

    So each term in the exp​ression for p[sH] is equal to [1/52] x [1/51].

    There are 51 terms, so

    p[sH] = 51 x [1/52] x [1/51] = 1/52.

    and so

    p[CA] = 12 x p[sH] = 12/52 = 3/13.

    In the proposed bet, the odds favor Davey by 4 1/3 to 1.

    If he gives 100 to 1 odds [a dollar for a penny], then

    Alex can expect to win about 23 cents on his penny.

    Once again, Alex has the better of the deal.

    Shall we call him a Smart Alex?

  11. when you pick the first chip and see that it is red or green, you now have more information about the remaining chips. You now must choose a chip from a smaller pool.
    Absolutely correct.

    [1] If no cup is removed, a particular pair of remaining cups match colors 12 of 26 times.

    [2] If a red cup is removed, a particular pair of remaining cups match colors 7 of 15 times.

    [3] If a green cup is removed, a particular pair of remaining cups match colors 5 of 11 times.

    [4] If we remove a cup 26 times [say cup 1] a particular pair of remaining cups match colors 12 of 26 times.

    Choose your interpretation of UR's 2nd question and you have your answer.

    I'm basing this on the Bayesean logic behind the popular Monty Hall Problem [url:341ca]http://en.wikipedia.org/wiki/Monty_Hall_problem
    In the Monty Hall Problem you are able to take guidance from the added knowledge.

    You can deduce that you'll win 2/3 of the time if you swap and 1/3 if you don't.

    If you think UR's 2nd question is like the MH problem, then let's give it a try:

    You pick a cup, say it's Cup 1, and I tell you it's green.

    Based on your knowledge that Cup 1 was green, which of your 6 options are you guided to choose?

    Cups 2 and 3

    Cups 2 and 4

    Cups 2 and 5

    Cups 3 and 4

    Cups 3 and 5

    Cups 4 and 5

  12. Assuming that two halves make a whole ...

    ... then here are your 8 people.

    [1] John and [2] Joan married and had three children: [3] Mary, [4] Marty and [5] Marie.

    Joan ran away with her tennis coach, leaving lonely John to do a very bad thing -- he married his daughter Mary.

    John and Mary had one child, [6] YOU

    Marty married the babe from across town and had two kids, [7] Ann and [8] Alex.

    Let's see if they account for everyone at the party.

    Mom and Dad are Mary and John.

    Grandparents are your mother's parents, John and Joan.

    Uncle and Auntie are your mother's siblings, Marty and Marie.

    Brother and Sister are your father's children, Mary, Marty and Marie.

    Niece and Nephew are your brother Marty's kids, Ann and Alex.

    OK I cheated a little ... Mary, Marty and Marie are half-siblings.

    But I gave you an extra half-sister, and two halves make a whole.

    Plus, you can now name 11 relations - 12 including YOU, all of whom eat just 1 of the 8 pieces of cake.

  13. It is not necessary for the train to come to a stop just because the fly did. The collision did cause the train to slow down (ever so slightly), however, it never comes to a complete stop. The train chugs along while the fly stops and reverses direction.

    When two elastic bodies collide, both energy and momentum are conserved.

    The fly was anything but elastic, becoming and remaining a simple

    grease spot, so in this case only momentum is conserved.

    Simply put,

    [Mass of fly] x [velocity change of fly] = [mass of train] x [velocity change of train]

    Let's say for argument's sake the train is ten times more massive than the fly.

    [That would be one big, m......f........ fly, by the way...]

    That gives you ... canceling mass of fly from both sides ...

    velocity change of fly = 10 x velocity change of train.

    the fly's velocity changed from +10 to -60 = 70 mph

    that means the train's velocity changed by 70/10 = 7 mph.

    The train continues moving forward, slowing from 60 mph to 53 mph.

    Even a fly weighing 1/10 the weight of the train won't stop it.

    Here's an interesting point.

    A detailed analysis of what happened to the fly reveals that it never

    actually came to rest! The first miniscule portion of the fly to contact the

    train instantaneously assumed the train's speed, producing a progressive

    collapse and deformation of the fly into a grease spot. The rear portions

    of the fly were still moving forward while its forward parts were traveling

    backwards. As a whole, the fly never had zero velocity, and thus technically

    never stopped.

  14. and hexadecimal (16) which uses A, B, C, D, and E to symbolize 11, 12, 13 14, and 15 as single digits
    Typo check: In hex, A-F represent 10-15.

    UR, I've never heard of base seven being used.

    Being curious [actually, I've been called worse,

    and with some justfication] what's base 7 used for?

  15. the actual positions of the cards are 100% chosen by the casino/gameshow... so there isnt random weighting involved- each could be as equally likely as the next
    I think we are agreeing loudly on this point.

    The positions of the colors are random [unknown to us] and the combinations of so many reds and so many greens --

    it doesn't matter that we used different numbers -- permit an enumeration of all possible,

    equally likely distributions.

    What's not 50-50 is the chance that any one particular cup is red or green.

    Count the number of times in my 26 equally likely color distributions that

    the first cup [for example] is red. It's 15. Not 13. -- or is green. It's 11. Not 13.

    Next, you see that in 7 of the 15 red-removed cases any 2 of the remaining 4 cups have the same color.

    In 5 of the 11 green-removed cases any 2 of the remaining 4 cups have the same color.

    If all you are saying is that 7/15 is different from 5/11, then the discussion is over and we can get some sleep.

    [Perhaps erroneously] I took your Case 2 question to mean in all cases when a cup is picked and removed from the group

    [not a particular case, like a red cup is picked first] does your chance of picking two matching colors

    differ from your chance of picking two matching colors when all 5 cups are there.

    My answer to that question is that the chances do not change.

    This follows from the observation you can make by inspecting the 26 equally likely distributions of 2 colors among 5 cups.

    Namely, that whatever two cups you inspect, 12/26 of the time they will be the same color.

    That statement is true whether any or all of the other three cups were removed initially or not.

    That is, there are no circumstances that force you to pick 2 particular cups that do not have a 12/26 chance of having the same color,

    simply because every pair of cups in the 26 equally likely cases has a 12/26 chance of a color match.

    Finally, it appears that if you eliminate the 5-red case [requiring at least 1 green]

    you will decrease the total distributions from 26 to 25,

    and the colors-will-match distributions from 12 to 11.

    That would change the answer for both Case 1 and Case 2 to 11/25 = 0.44.

  16. In Case 2, you pick a cup -- and without knowledge this is a random pick -- and then eliminate that cup.

    Since there are more red than green cups [in the sample space I used, where 5 reds were possible],

    the odds of picking a red cup first are different from the odds of picking a green cup first, and

    the odds of getting a pair after picking a red cup differ from the odds of getting a pair after picking a green

    Not that that really matters, I just made a note of it.

    In the space of all possible outcomes for Case 2, [that includes 15 times a red cup is picked first and 11 times that a green is picked first] the probability of getting a pair after one cup is eliminated is the same as for Case 1.

    In either case, it's simply the odds that any two cups are the same color: 12/26 = .461

    You could take away three cups at first then ask the odds that the remaining cups are a match.

    Same result.

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