Brain Teasers at Xmas
Posted by: Don Atkinson on 23 December 2010
Brain Teasers at Xmas
Xmas time - and many of us will be off on holiday or meeting up with friends and family. For those with a bit of time on their hands, I thought I would post a dozen (12 days of Xmas ?) brain teasers to help keep your minds in gear.
All are taken from the Brain Teaser thread from a few years back and credit is given to the original poster where this is other than me. Ken c still posts here, but BAM and Matthew T….??
None of these teasers are “trick” questions, but you will need to read them carefully in order to understand some of them. Discuss at leisure......
I know it’s not as exciting as today’s hi-tech electronic games, but I hope it helps to keep some of you amused over Xmas, and as Ken c would say – “enjoy”
Cheers
Don
Xmas time - and many of us will be off on holiday or meeting up with friends and family. For those with a bit of time on their hands, I thought I would post a dozen (12 days of Xmas ?) brain teasers to help keep your minds in gear.
All are taken from the Brain Teaser thread from a few years back and credit is given to the original poster where this is other than me. Ken c still posts here, but BAM and Matthew T….??
None of these teasers are “trick” questions, but you will need to read them carefully in order to understand some of them. Discuss at leisure......
I know it’s not as exciting as today’s hi-tech electronic games, but I hope it helps to keep some of you amused over Xmas, and as Ken c would say – “enjoy”
Cheers
Don
Posted on: 23 December 2010 by Don Atkinson
#1 The Explorer
An explorer set off on a journey. He walked a mile south, a mile east and a mile north. At this point he was back at his start. Where on earth was his starting point? OK, other than the North Pole, which is pretty obvious, where else could he have started this journey
?
Cheers
Don
An explorer set off on a journey. He walked a mile south, a mile east and a mile north. At this point he was back at his start. Where on earth was his starting point? OK, other than the North Pole, which is pretty obvious, where else could he have started this journey
?
Cheers
Don
Posted on: 23 December 2010 by Don Atkinson
#2 Small Reservoir (BAM)
A woman is sitting in a boat in a small reservoir. In the boat with her is a hemp sack containing the dead body of her audiophile husband. She had become frustrated with her obsessive partner mainly due to the proliferation of ugly black boxes and metalwork that had taken over her living room. Not to mention the brick dust and ill fitting carpets where he installed the make-shift mains spur; nor to mention the devastation of her beautiful flower beds where he had insisted on driving a dozen copper pipes into the ground. The final straw came when, at the recommendation of an old school friend in the business (a friend before she met HIM), Ideal Home dropped in to offer to do a feature. Shocked by the hifi carnage they declined to do the feature.
Anyhow, I digress. She has weighed the sack down with two 135s and the twisted remains of his Mana stands and sewn it tightly with NACA5 (ensuring correct direction in the weave) to ensure he will sink without trace. Whilst securing the parcel she glances over to the reservoir wall and notices a water level marker. With a major struggle she manages to heave the sack of hubby and hifi over board. After a while she settles back in the dingy and smokes a well-earned cigarette. The reservoir wall catches her eye again; she notices the height of the water line has changed.
Has the water risen or fallen against its original level on the water level marker?
Cheers
Don
A woman is sitting in a boat in a small reservoir. In the boat with her is a hemp sack containing the dead body of her audiophile husband. She had become frustrated with her obsessive partner mainly due to the proliferation of ugly black boxes and metalwork that had taken over her living room. Not to mention the brick dust and ill fitting carpets where he installed the make-shift mains spur; nor to mention the devastation of her beautiful flower beds where he had insisted on driving a dozen copper pipes into the ground. The final straw came when, at the recommendation of an old school friend in the business (a friend before she met HIM), Ideal Home dropped in to offer to do a feature. Shocked by the hifi carnage they declined to do the feature.
Anyhow, I digress. She has weighed the sack down with two 135s and the twisted remains of his Mana stands and sewn it tightly with NACA5 (ensuring correct direction in the weave) to ensure he will sink without trace. Whilst securing the parcel she glances over to the reservoir wall and notices a water level marker. With a major struggle she manages to heave the sack of hubby and hifi over board. After a while she settles back in the dingy and smokes a well-earned cigarette. The reservoir wall catches her eye again; she notices the height of the water line has changed.
Has the water risen or fallen against its original level on the water level marker?
Cheers
Don
Posted on: 23 December 2010 by Don Atkinson
#3 Game Show (BAM)
Alright, here's an old one so I hope you haven't heard the answer already. If you haven't it is quite interesting. Enjoy!
Late one cold, rainy night in November after a few pints and a rather dubious curry you flop down onto your favourite listening couch and turn on your Naim system. Ah...that's better. But even the PRaT isn't enough to keep your eyes from closing and you soon fall into a deep, deep slumber and start to dream..
.
Congratulations! You have been selected as a participant in a very popular national TV gameshow. This is your first time on TV and on such a show and you are overwhelmed with excitement and nervousness. The gameshow host is none other than Paul Stephenson. Dressed in a gold lame suit with sequins, standing centre-stage on a Fraim. The grand prize: a Naim NAP500 and installation in your home by Roy George himself. Your heart pounds with excitement.
You find the first rounds easy and before long the other contestants have been eliminated and you have made it to the final challenge. The audience go wild! You try hard to look at them through the bright spot lights and recognize them as your chums from the Naim Forum - all clapping and cheering you on. What a night!
Now the final challenge begins. The lights dim and the cheers of the crowd die down. Paul shows you three doors numbered 1, 2 and 3. He says that the NAP500 is hidden behind one of the doors. You must choose which one. If you choose correctly you win the NAP500. If not you win Paul's hideous suit. The tension mounts. The audience can't contain themselves: shouts begin..."door 1"..."no door 2"...etc. You hesitate. Paul urges you to make a choice. Finally you choose door number 3 (after your existing Nait 3 system). A green light comes on over door 3. Oh no...did I choose wisely...
A hush comes over the theatre as Paul walks over to door number 1 and motions to open it. The atmosphere can be cut with a knife. Slowly, Paul opens door 1 to reveal nothing! Phew that was lucky. The crowd bursts into a relieved cheer. But soon Paul has gripped the handle of door 2 and the crowd go silent. You can hear a pin drop.
The tension is unbearable...
Suddenly Paul stops turning the handle of door 2 and turns towards you. He says he is in a good mood tonight and wants to help you as much as he can. He offers to do you a favour and allow you to change your selection. You can now stick with your original choice...door 3 or switch to door 2. It is up to you and you have just 10 seconds to decide. The audience erupts! "door 2, go for door 2"..."no, no stick with door 3"...
You have 5 seconds left. You are sweating. Everyone is hanging on your next words. Do you stick with door 3 or switch to door 2?
Cheers
Don
Alright, here's an old one so I hope you haven't heard the answer already. If you haven't it is quite interesting. Enjoy!
Late one cold, rainy night in November after a few pints and a rather dubious curry you flop down onto your favourite listening couch and turn on your Naim system. Ah...that's better. But even the PRaT isn't enough to keep your eyes from closing and you soon fall into a deep, deep slumber and start to dream..
.
Congratulations! You have been selected as a participant in a very popular national TV gameshow. This is your first time on TV and on such a show and you are overwhelmed with excitement and nervousness. The gameshow host is none other than Paul Stephenson. Dressed in a gold lame suit with sequins, standing centre-stage on a Fraim. The grand prize: a Naim NAP500 and installation in your home by Roy George himself. Your heart pounds with excitement.
You find the first rounds easy and before long the other contestants have been eliminated and you have made it to the final challenge. The audience go wild! You try hard to look at them through the bright spot lights and recognize them as your chums from the Naim Forum - all clapping and cheering you on. What a night!
Now the final challenge begins. The lights dim and the cheers of the crowd die down. Paul shows you three doors numbered 1, 2 and 3. He says that the NAP500 is hidden behind one of the doors. You must choose which one. If you choose correctly you win the NAP500. If not you win Paul's hideous suit. The tension mounts. The audience can't contain themselves: shouts begin..."door 1"..."no door 2"...etc. You hesitate. Paul urges you to make a choice. Finally you choose door number 3 (after your existing Nait 3 system). A green light comes on over door 3. Oh no...did I choose wisely...
A hush comes over the theatre as Paul walks over to door number 1 and motions to open it. The atmosphere can be cut with a knife. Slowly, Paul opens door 1 to reveal nothing! Phew that was lucky. The crowd bursts into a relieved cheer. But soon Paul has gripped the handle of door 2 and the crowd go silent. You can hear a pin drop.
The tension is unbearable...
Suddenly Paul stops turning the handle of door 2 and turns towards you. He says he is in a good mood tonight and wants to help you as much as he can. He offers to do you a favour and allow you to change your selection. You can now stick with your original choice...door 3 or switch to door 2. It is up to you and you have just 10 seconds to decide. The audience erupts! "door 2, go for door 2"..."no, no stick with door 3"...
You have 5 seconds left. You are sweating. Everyone is hanging on your next words. Do you stick with door 3 or switch to door 2?
Cheers
Don
Posted on: 23 December 2010 by Don Atkinson
#4 The Baron's Treasure
Baron Von Stephenson kept his gold treasure (fairly got by manufacturing hi quality electronics) in a treasure house. In each room of the treasure house were as many chests as there were rooms. In each chest there were as many gold coins, as there were chests in that room. All the gold coins were of the same size and value.
When he died (ok, this is a futuristic story set in the year 2252), the Baron's will was that his favourite Forum member (Guesses on a postcard please!!) should receive one chest of gold coins. The remaining coins were to be divided equally between the Baron's three forum administrators, Paul Des, Doug G and Paul Dar .
The three administrators were proud and fierce men who would definitely resort to bloodshed if the coins could not be divided equally.
The question is simply: -
a) Was there blood shed.
b) Was there no blood shed.
c) Is there no way of knowing whether there was blood shed or not.
PS. The proof is the real requirement, not simply a one in three guess.
Cheers
Don
Baron Von Stephenson kept his gold treasure (fairly got by manufacturing hi quality electronics) in a treasure house. In each room of the treasure house were as many chests as there were rooms. In each chest there were as many gold coins, as there were chests in that room. All the gold coins were of the same size and value.
When he died (ok, this is a futuristic story set in the year 2252), the Baron's will was that his favourite Forum member (Guesses on a postcard please!!) should receive one chest of gold coins. The remaining coins were to be divided equally between the Baron's three forum administrators, Paul Des, Doug G and Paul Dar .
The three administrators were proud and fierce men who would definitely resort to bloodshed if the coins could not be divided equally.
The question is simply: -
a) Was there blood shed.
b) Was there no blood shed.
c) Is there no way of knowing whether there was blood shed or not.
PS. The proof is the real requirement, not simply a one in three guess.
Cheers
Don
Posted on: 23 December 2010 by Don Atkinson
#5 Odd Ball?
I have twelve balls that LOOK identical but one (and only one) is either heavier or lighter than the rest. Using a pair of scales, I can compare the weight of any combination of balls that I chose. What is the MINIMUM number of weighings that I need to make, in order to identify the odd ball and decide whether it is heavy or light?
PS 'scales' = those old fashioned ones that look a bit like the Scales of Justice
Cheers
Don
I have twelve balls that LOOK identical but one (and only one) is either heavier or lighter than the rest. Using a pair of scales, I can compare the weight of any combination of balls that I chose. What is the MINIMUM number of weighings that I need to make, in order to identify the odd ball and decide whether it is heavy or light?
PS 'scales' = those old fashioned ones that look a bit like the Scales of Justice
Cheers
Don
Posted on: 23 December 2010 by Don Atkinson
#6 How Far is it to Salisbury?
Ok guys,
Whilst you are trying to figure out how to do it in three (and I think it's very decent of Duncan F and others to sit tight whilst yet others try to figure it out) here's a much more straightforward one.
Naim have two delivery vans that shuttle between Salisbury and their favourite dealer. (Ok, ok, in the original version it was 'two ships operate a ferry service across a river….')
Naim have two delivery vans that shuttle between Salisbury and their favourite dealer. On a particular day, one van leaves Salisbury bound for the dealer, whilst at the same time the other van leaves the dealer, bound for Salisbury. Both vans follow the same route and pass each other (giving the famous 'Naim Salute') 30 miles from the dealer's. At their initial destinations each van takes 15 minutes to load/unload. On the return journey, following the same route, the vans pass each other (giving the famous 'Naim Salute') 15 miles from Salisbury.
How far is it from Salisbury to the dealer's ?
Assume that each van travels at a constant speed and that acceleration/deceleration is allowed for in the 15 minute turn round time.
Cheers
Don
Ok guys,
Whilst you are trying to figure out how to do it in three (and I think it's very decent of Duncan F and others to sit tight whilst yet others try to figure it out) here's a much more straightforward one.
Naim have two delivery vans that shuttle between Salisbury and their favourite dealer. (Ok, ok, in the original version it was 'two ships operate a ferry service across a river….')
Naim have two delivery vans that shuttle between Salisbury and their favourite dealer. On a particular day, one van leaves Salisbury bound for the dealer, whilst at the same time the other van leaves the dealer, bound for Salisbury. Both vans follow the same route and pass each other (giving the famous 'Naim Salute') 30 miles from the dealer's. At their initial destinations each van takes 15 minutes to load/unload. On the return journey, following the same route, the vans pass each other (giving the famous 'Naim Salute') 15 miles from Salisbury.
How far is it from Salisbury to the dealer's ?
Assume that each van travels at a constant speed and that acceleration/deceleration is allowed for in the 15 minute turn round time.
Cheers
Don
Posted on: 23 December 2010 by Don Atkinson
#7 The Boring Sphere - or Another Load of Balls
A six-inch long hole is drilled right through a sphere, along a diameter. What is the volume of solid material left in the resultant bead?
Cheers
Don
A six-inch long hole is drilled right through a sphere, along a diameter. What is the volume of solid material left in the resultant bead?
Cheers
Don
Posted on: 23 December 2010 by Don Atkinson
#8 Ladder (BAM)
Well, I've been thinking of another puzzle to keep you occupied in the run-up to Christmas. Here 'tis:
'Twas the night before Christmas and in the Naim factory not a creature was stirring except for... In an attempt to discover the secrets of Naim's new NAP500 a team of Sony engineers (the ones mentioned in that other post who collect the musical electrons off the floor that have fallen out of unsoldered speaker cable strands) decided to gain illegal entry to the Naim factory. Oh the shame of it!
They arrive at the factory in the dead of night and decide to try to gain entry via the roof. Naturally they aren't carrying a ladder because this would arouse suspicion among the locals in Salisbury. So they search for one and eventually find an old wooden, slightly rotten set of rungs. The ladder has length L. The factory roof is hard to access, even with a ladder, and on their first attempt the ladder crackles and threatens to break. They stop climbing and wonder what to do. Scouting for a way in they find a wall against which a large, cubic crate has been left of side 1m. They reason that if they position the ladder so that it touches the ground, the wall and the edge of the crate that this will provide sufficient support to prevent the ladder from breaking. Good.
Being exacting engineers and slaves to planning they first decide to calculate the exact distance that they must place the foot of the ladder away from the side of the crate so that it will touch both the wall and the crate edge. Can they work it out before sunrise?
In terms of the ladder length L what is the horizontal distance the foot of the ladder must be placed away from the side of the crate? Assume the ground is horizontal, the wall vertical and the crate a perfect cube.
The winner will have the most elegant formula.
Cheers
Don
Well, I've been thinking of another puzzle to keep you occupied in the run-up to Christmas. Here 'tis:
'Twas the night before Christmas and in the Naim factory not a creature was stirring except for... In an attempt to discover the secrets of Naim's new NAP500 a team of Sony engineers (the ones mentioned in that other post who collect the musical electrons off the floor that have fallen out of unsoldered speaker cable strands) decided to gain illegal entry to the Naim factory. Oh the shame of it!
They arrive at the factory in the dead of night and decide to try to gain entry via the roof. Naturally they aren't carrying a ladder because this would arouse suspicion among the locals in Salisbury. So they search for one and eventually find an old wooden, slightly rotten set of rungs. The ladder has length L. The factory roof is hard to access, even with a ladder, and on their first attempt the ladder crackles and threatens to break. They stop climbing and wonder what to do. Scouting for a way in they find a wall against which a large, cubic crate has been left of side 1m. They reason that if they position the ladder so that it touches the ground, the wall and the edge of the crate that this will provide sufficient support to prevent the ladder from breaking. Good.
Being exacting engineers and slaves to planning they first decide to calculate the exact distance that they must place the foot of the ladder away from the side of the crate so that it will touch both the wall and the crate edge. Can they work it out before sunrise?
In terms of the ladder length L what is the horizontal distance the foot of the ladder must be placed away from the side of the crate? Assume the ground is horizontal, the wall vertical and the crate a perfect cube.
The winner will have the most elegant formula.
Cheers
Don
Posted on: 23 December 2010 by Don Atkinson
#9 And another little, simple one... (Ken c)
prove that the product of 4 consecutive numbers is always one less than a square number.
so for example: 2 * 3 * 4 * 5 = 120 which is 1 less than 11^2
Cheers
Don
prove that the product of 4 consecutive numbers is always one less than a square number.
so for example: 2 * 3 * 4 * 5 = 120 which is 1 less than 11^2
Cheers
Don
Posted on: 23 December 2010 by Don Atkinson
#10 Tying Nanny up (BAM)
I fear Ken may have a breakthrough brewing for the ladder puzzle so here's another problem as an interlude.
Near a small town with a big church in Wiltshire, an audio industry worker named Paul supplements his meagre salary with part-time farming. Paul owns a circular field of grass of unit radius and he also owns a very hungry goat from which he derives milk for cheese. Paul wishes to tie the goat to an existing post on the circumference of the field and wants to manage the growth of the grass so the goat doesn't decimate it too quickly. He therefore decides to use just enough rope so that the goat can only eat 50% of the grass.
What must the length of the rope be? Assume the distance between the jaws of the goat and the point of attachment of the rope is insignificant.
Cheers
Don
I fear Ken may have a breakthrough brewing for the ladder puzzle so here's another problem as an interlude.
Near a small town with a big church in Wiltshire, an audio industry worker named Paul supplements his meagre salary with part-time farming. Paul owns a circular field of grass of unit radius and he also owns a very hungry goat from which he derives milk for cheese. Paul wishes to tie the goat to an existing post on the circumference of the field and wants to manage the growth of the grass so the goat doesn't decimate it too quickly. He therefore decides to use just enough rope so that the goat can only eat 50% of the grass.
What must the length of the rope be? Assume the distance between the jaws of the goat and the point of attachment of the rope is insignificant.
Cheers
Don
Posted on: 23 December 2010 by Don Atkinson
#11 Another set of circles
It’s pretty obvious that the maximum number of different sized circles (excluding infinitely large circles that have become straight lines!) that can be made to 'just touch' one another is four. (each and every circle just touches the other three).
Three circles A, B and C have radii of 1, 2 and 3 respectively. What are the radii of the two 'fourth' circles, that can be made to just touch each of A, B and C. (note the two 'fourth' circles will not touch each other, ‘cos that would break the golden rule!!)
Oh! BTW, there is a standard way and an elegant way to solve this little problem. The normal way will do for most, but in the case of Bam………..
Cheers
Don
It’s pretty obvious that the maximum number of different sized circles (excluding infinitely large circles that have become straight lines!) that can be made to 'just touch' one another is four. (each and every circle just touches the other three).
Three circles A, B and C have radii of 1, 2 and 3 respectively. What are the radii of the two 'fourth' circles, that can be made to just touch each of A, B and C. (note the two 'fourth' circles will not touch each other, ‘cos that would break the golden rule!!)
Oh! BTW, there is a standard way and an elegant way to solve this little problem. The normal way will do for most, but in the case of Bam………..
Cheers
Don
Posted on: 23 December 2010 by Don Atkinson
#12 Balls in a box (Matthew T)
I have a box 5cm x 5cm x 10cm and spherical balls of diameter 1cm. What is the maximum number of balls can I fit in the box?
All dimensions are exact (internal dimensions for the box) and the box has a lid that must close.
Cheers
Don
I have a box 5cm x 5cm x 10cm and spherical balls of diameter 1cm. What is the maximum number of balls can I fit in the box?
All dimensions are exact (internal dimensions for the box) and the box has a lid that must close.
Cheers
Don
Posted on: 23 December 2010 by Tarquin Maynard - Portly
aaaaaaaargh
Posted on: 23 December 2010 by Don Atkinson
quote:aaaaaaaargh
Cheer up!! - its Xmas!
Cheers
Don
Posted on: 23 December 2010 by TomK
quote:Originally posted by Don Atkinson:
#9 And another little, simple one... (Ken c)
prove that the product of 4 consecutive numbers is always one less than a square number.
so for example: 2 * 3 * 4 * 5 = 120 which is 1 less than 11^2
Cheers
Don
This is hardly a brain teaser. It's a university level exercise in pure mathematics. If you can prove this and don't have a maths degree enrol in a maths course as soon as you can. Look forward to taking pleasure in finding out that e raised to the power i pi = -1. It just doesn't get any better than this for fellow geeks.
Posted on: 23 December 2010 by Don Atkinson
quote:And another little, simple one...
Tom, I blame ken c.....he said it was "simple"........to my mind, it was a brain-teaser.
(but more like "A" level stuff). Perhaps "simple" refered to the question rather than the answer?BTW, nice to be reminded about the relationship between e, i, pi and 1
Merry Xmas
Don
PS I do accept that half of these specific "brain teasers" are little more than "A" level maths questions dressed up a bit. But the other half should have a wider appeal. Of course, knowing which is which is half the problem........
Posted on: 28 December 2010 by Don Atkinson
The following (brain numbing?) question comes up during every flying training course.
It applies to all aeroplanes, but because flying training starts off in small, single-engined aeroplanes, it usually involves decision-making regarding the "mother-in-law", who is the only other occupant of the aeroplane.
The engine has failed and the aeroplane is gliding. You are looking for a suitable field in which to land and trying to decide what else you might do to increase YOUR chance of survival. The mother-in-law is a hefty 250lbs of (not so prime) beef.
Would it be best to chuck her out to reduce the weight of the aeroplane (which is already below its maximumum authorised landing weight), keep her on board as ballast, or doesn't it really matter?
Cheers
Don
PS if it makes you feel any better, you could assume she has a parachute...........
It applies to all aeroplanes, but because flying training starts off in small, single-engined aeroplanes, it usually involves decision-making regarding the "mother-in-law", who is the only other occupant of the aeroplane.
The engine has failed and the aeroplane is gliding. You are looking for a suitable field in which to land and trying to decide what else you might do to increase YOUR chance of survival. The mother-in-law is a hefty 250lbs of (not so prime) beef.
Would it be best to chuck her out to reduce the weight of the aeroplane (which is already below its maximumum authorised landing weight), keep her on board as ballast, or doesn't it really matter?
Cheers
Don
PS if it makes you feel any better, you could assume she has a parachute...........
Posted on: 28 December 2010 by Fred Mulder
Hi Don,
I'll give some a go, thanks for you confidence in the forum
1)
in sea: ask jacques cousteau (close)
in the sky: ask neil armstrong (closer)
on earth: ask Charles Marie de La Condamine
2)
wrong education.. does the cigarette has something to do with it?
3)
too much text, sorry
4)
easy, Avole
5)
aaaa = bbbb
aaaa > cxcc
c > x
6 and beyond: perhaps I'll try later. Must stop now, avoid pondering at this time
Cheers, Fred
I'll give some a go, thanks for you confidence in the forum
1)
in sea: ask jacques cousteau (close)
in the sky: ask neil armstrong (closer)
on earth: ask Charles Marie de La Condamine
2)
wrong education.. does the cigarette has something to do with it?
3)
too much text, sorry
4)
easy, Avole
5)
aaaa = bbbb
aaaa > cxcc
c > x
6 and beyond: perhaps I'll try later. Must stop now, avoid pondering at this time
Cheers, Fred
Posted on: 29 December 2010 by Don Atkinson
Fred,
1.
Old Charlie spent most of his reasearch time on the equator.
Now this is interesting because this is the only part if the world where we can walk a mile south, a mile east, a mile north and actually end up a mile east of where we started!
2. The faggs have nothing to do with the physics of the boat and its load.
3. To cut BAM's long story short -
Three doors. Behind one door is the "Golden" prise of a NAP500. The other two doors are enpty - you win a second-hand gold coloured lame suit!
Pick any door. Gameshow host opens one of the other doors to reveal it is empty. Gameshow host then gives you (the contestant) the chance to change your mind. ie you can stick with your first choice, or, you can select the other door that hasn't yet been opened.
What's your best strategy to improve you chances of winning the car.
4- and onwards - another day
Cheers
Don
1.
quote:on earth: ask Charles Marie de La Condamine
Old Charlie spent most of his reasearch time on the equator.
Now this is interesting because this is the only part if the world where we can walk a mile south, a mile east, a mile north and actually end up a mile east of where we started!
2. The faggs have nothing to do with the physics of the boat and its load.
3. To cut BAM's long story short -
Three doors. Behind one door is the "Golden" prise of a NAP500. The other two doors are enpty - you win a second-hand gold coloured lame suit!
Pick any door. Gameshow host opens one of the other doors to reveal it is empty. Gameshow host then gives you (the contestant) the chance to change your mind. ie you can stick with your first choice, or, you can select the other door that hasn't yet been opened.
What's your best strategy to improve you chances of winning the car.
4- and onwards - another day
Cheers
Don
Posted on: 30 December 2010 by Fred Mulder
Hi Don,
I'll think about it. Haven't got a clue at this moment.. I've also read the full version, which was nice. In respond and appriciation for the effort, here's a story for you. To kill some time, waiting for an answer ;-)
Cheers, Fred
By coincidence you're a custom officer, specialized in consumer goods at a international harbor: For Naim's latest product launch heaps of containers with the new DAC555 are about getting shipped around the world.
Oh dear, by telephone you're informed that one container has counterfit DAC555's. Besides there musical performance it appears that the weight is just a wee bit off, due to the bad connection you can't hear if they are heavier or lighter. No time to waste. To avoid a delayed product release the containers must be loaded soon, cargo ships are already preparing there leave.
Naims reputation and happy customers depend on you: By exception you're allowed to use a weightscale from your colleagues. It's similar to the digital weightscales at home, but bigger. How do you determine which container has the counterfit products.
You may fill in the blanks when it makes things easier. Oh, you're allowed to use the scale just once.
Unfortunaly no spell check, typing in the train..
I'll think about it. Haven't got a clue at this moment.. I've also read the full version, which was nice. In respond and appriciation for the effort, here's a story for you. To kill some time, waiting for an answer ;-)
Cheers, Fred
By coincidence you're a custom officer, specialized in consumer goods at a international harbor: For Naim's latest product launch heaps of containers with the new DAC555 are about getting shipped around the world.
Oh dear, by telephone you're informed that one container has counterfit DAC555's. Besides there musical performance it appears that the weight is just a wee bit off, due to the bad connection you can't hear if they are heavier or lighter. No time to waste. To avoid a delayed product release the containers must be loaded soon, cargo ships are already preparing there leave.
Naims reputation and happy customers depend on you: By exception you're allowed to use a weightscale from your colleagues. It's similar to the digital weightscales at home, but bigger. How do you determine which container has the counterfit products.
You may fill in the blanks when it makes things easier. Oh, you're allowed to use the scale just once.
Unfortunaly no spell check, typing in the train..
Posted on: 30 December 2010 by DaveBk
I'll have a go at number 2...
For the fully loaded boat to float it must displace more water than it weighs. For the unfortunate hi-fi buff to sink he, plus all the kit, must weigh more than he displaces.
Once he's sunk, the total water displaced must be lower than when he was floating in the boat so the water level in the lake would be lower.
Correct?
For the fully loaded boat to float it must displace more water than it weighs. For the unfortunate hi-fi buff to sink he, plus all the kit, must weigh more than he displaces.
Once he's sunk, the total water displaced must be lower than when he was floating in the boat so the water level in the lake would be lower.
Correct?
Posted on: 30 December 2010 by winkyincanada
quote:Originally posted by DaveBk:
I'll have a go at number 2...
For the fully loaded boat to float it must displace more water than it weighs. For the unfortunate hi-fi buff to sink he, plus all the kit, must weigh more than he displaces.
Once he's sunk, the total water displaced must be lower than when he was floating in the boat so the water level in the lake would be lower.
Correct?
I think so. Provided the thing thrown overboard sinks (i.e. is more dense than water) then it will displace less volume than it did when being supported by the boat where the volume is the volume of water that weighs the same as the object. If the thing thrown overboard floats, then the water level doesn't change.
Posted on: 30 December 2010 by winkyincanada
quote:Originally posted by Don Atkinson:
#3 Game Show (BAM)
Alright, here's an old one so I hope you haven't heard the answer already. If you haven't it is quite interesting. Enjoy!
Late one cold, rainy night in November after a few pints and a rather dubious curry you flop down onto your favourite listening couch and turn on your Naim system. Ah...that's better. But even the PRaT isn't enough to keep your eyes from closing and you soon fall into a deep, deep slumber and start to dream..
.
Congratulations! You have been selected as a participant in a very popular national TV gameshow. This is your first time on TV and on such a show and you are overwhelmed with excitement and nervousness. The gameshow host is none other than Paul Stephenson. Dressed in a gold lame suit with sequins, standing centre-stage on a Fraim. The grand prize: a Naim NAP500 and installation in your home by Roy George himself. Your heart pounds with excitement.
You find the first rounds easy and before long the other contestants have been eliminated and you have made it to the final challenge. The audience go wild! You try hard to look at them through the bright spot lights and recognize them as your chums from the Naim Forum - all clapping and cheering you on. What a night!
Now the final challenge begins. The lights dim and the cheers of the crowd die down. Paul shows you three doors numbered 1, 2 and 3. He says that the NAP500 is hidden behind one of the doors. You must choose which one. If you choose correctly you win the NAP500. If not you win Paul's hideous suit. The tension mounts. The audience can't contain themselves: shouts begin..."door 1"..."no door 2"...etc. You hesitate. Paul urges you to make a choice. Finally you choose door number 3 (after your existing Nait 3 system). A green light comes on over door 3. Oh no...did I choose wisely...
A hush comes over the theatre as Paul walks over to door number 1 and motions to open it. The atmosphere can be cut with a knife. Slowly, Paul opens door 1 to reveal nothing! Phew that was lucky. The crowd bursts into a relieved cheer. But soon Paul has gripped the handle of door 2 and the crowd go silent. You can hear a pin drop.
The tension is unbearable...
Suddenly Paul stops turning the handle of door 2 and turns towards you. He says he is in a good mood tonight and wants to help you as much as he can. He offers to do you a favour and allow you to change your selection. You can now stick with your original choice...door 3 or switch to door 2. It is up to you and you have just 10 seconds to decide. The audience erupts! "door 2, go for door 2"..."no, no stick with door 3"...
You have 5 seconds left. You are sweating. Everyone is hanging on your next words. Do you stick with door 3 or switch to door 2?
Cheers
Don
This is the Monty Hall problem. The correct thing to do is to change your choice of doors. The host's selection of an empty door is contingent on the door you first chose and on the host's knowledge of the door with the prize. He always reveals an empty door. It is not random, and adds information to the player. The best use of this new information is to change.
It is counter-intuitive to many and a bit hard to explain. Think of it like this. If you have originally chosen the correct door (on average, 1/3 of the time you will do this), then changing will make you lose. But if you have chosen the wrong door originally (on average 2/3 of the time you will do this), then changing will make you win. The conclusion is that you will win 2/3 of the time if you change doors, but only 1/3 of the time if you don't.
Another way to think of it is to consider that sticking with the door you first chose sticks you with the original probability i.e. 1 in 3 chance of winning. The host revealing an empty door doesn't change this. The ONLY way to change this is if you change doors. It actually gives you a 2/3 chance of winning (1 minus 1/3, not 1/2 as might seem obvious).
Posted on: 30 December 2010 by winkyincanada
quote:Originally posted by Don Atkinson:
#1 The Explorer
An explorer set off on a journey. He walked a mile south, a mile east and a mile north. At this point he was back at his start. Where on earth was his starting point? OK, other than the North Pole, which is pretty obvious, where else could he have started this journey
?
Cheers
Don
Almost exactly 1 + 1/(2*pi) miles way from the South Pole (slight error in my formula due to me not taking surface curvature into account - he'd actually need to be very, very, very slightly further away). Such that his walk of 1 mile east comprised full lap of the pole. He walks one mile south, laps the pole then walks back north along his original route. The shape of his walk looks a little like a keyhole with the South Pole in the middle of the circle bit.
Interestingly, he could start anywhere along the correct parallel of latitude, making this answer more general than the solution at the North pole.
Posted on: 30 December 2010 by fatcat
Winky
The odds on the contestant winning are always 1 in 2. It makes no difference if he changes or not.
The fact that the host ALWAYS opens an empty door means there is NEVER a 1 in 3 chance. ALWAYS a 1 in 2
The odds on the contestant winning are always 1 in 2. It makes no difference if he changes or not.
The fact that the host ALWAYS opens an empty door means there is NEVER a 1 in 3 chance. ALWAYS a 1 in 2