A Fistful of Brain Teasers
Posted by: Don Atkinson on 13 November 2017
A Fistful of Brain Teasers
For those who are either non-British, or under the age of 65………. The UK used to have a brilliant system of currency referred to as “Pounds, Shillings and Pence”. Simplified to £ ״ s ״ d. No! Don’t ask me why the “Pence” symbol is a “d”, just learn it and remember it !
A £ comprised 20 Shillings and a Shilling comprised 12 Pence. Thus a £ comprised 240 Pence. I reckon that both Microsoft and Apple would have difficulty with these numbers in their spreadsheets, more so if we included Guineas, Crowns, Half-Crowns and Florins. However, I digress..............
The purpose of the explanation is to assist with the first two or three teasers that follow. So just to ensure a reasonable comprehension has been grasped…. ….. if each of three children has £3 − 7s − 9d, then collectively they have £10 − 3s − 3d Got the idea ? Good ! Just try 5 children, two each with £4 − 15s − 8d and three each with £3 − 3s − 4d. How much do they have between them ? (this isn’t the first brain teaser, just the basic introduction with some “homework”, the Teasers follow)
HI mulberry,
Regardless of whether your interpretation of NFG's puzzle is correct or not, I think your interpretation is a worthy puzzle in itself.
ie how far appart should the posts be if the area of the overlapping grass circles is equal to 10% of the combined grass areas ie c. 786 sqm
Nice one 
Another one for the "linguists" ...............
PS. I don't really like these ones, but clearly others do
Don Atkinson posted:HI mulberry,
Regardless of whether your interpretation of NFG's puzzle is correct or not, I think your interpretation is a worthy puzzle in itself.
ie how far appart should the posts be if the area of the overlapping grass circles is equal to 10% of the combined grass areas ie c. 786 sqm
Nice one
Has anybody else got an answer to Mulberry's interpretation of NFG's puzzle about the two goats ?
I have a formula that gives a result in the region of 47.5m (*) but have yet to check my workings...........
(*) I have got a few more decimal places, but the figure quoted is the "ball-park" figure !
I have checked my workings and they look good.
I have also used the figure of 47.5m (plus a few decimal places) to validate that the overlap between two circles radii 40m and 30m, this far apart, is in fact 10% of their combined area. And it is.
But my calcs might still be wrong and Mulberry's interpretation might not be the required solution
Anybody got a better figure, or perhaps some elegant solution ?
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 the TV. Ah...that's better. But Have I Got News For You 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.
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! What a night!
Now the final challenge begins. The lights dim and the cheers of the crowd die down. Ant & Dec show you three doors numbered 1, 2 and 3. They say that the Porsche is hidden behind one of the doors. You must choose which one. If you choose correctly you win the Porsche. If not, you win a goat. The tension mounts. The audience can't contain themselves: shouts begin..."door 1"..."no door 2"...etc. You hesitate. Ant urges you to make a choice. Finally you choose door number 3. A green light comes on over door 3. Oh no...did I choose wisely...
A hush comes over the theatre as Dec walks over to door number 1 and motions to open it. The atmosphere can be cut with a knife. Slowly, Dec opens door 1 to reveal a goat! Phew that was lucky. The crowd bursts into a relieved cheer. But soon Ant has gripped the handle of door 2 and the crowd go silent. You can hear a pin drop.
The tension is unbearable...
Suddenly Ant 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?
As I said, it's an old one, so you no doubt know the best thing to do and that's fine - just post your option. But..
...top marks go to the best explanation for your decision to open Door No............
Don Atkinson posted: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 the TV. Ah...that's better. But Have I Got News For You 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.
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! What a night!
Now the final challenge begins. The lights dim and the cheers of the crowd die down. Ant & Dec show you three doors numbered 1, 2 and 3. They say that the Porsche is hidden behind one of the doors. You must choose which one. If you choose correctly you win the Porsche. If not, you win a goat. The tension mounts. The audience can't contain themselves: shouts begin..."door 1"..."no door 2"...etc. You hesitate. Ant urges you to make a choice. Finally you choose door number 3. A green light comes on over door 3. Oh no...did I choose wisely...
A hush comes over the theatre as Dec walks over to door number 1 and motions to open it. The atmosphere can be cut with a knife. Slowly, Dec opens door 1 to reveal a goat! Phew that was lucky. The crowd bursts into a relieved cheer. But soon Ant has gripped the handle of door 2 and the crowd go silent. You can hear a pin drop.
The tension is unbearable...
Suddenly Ant 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?
As I said, it's an old one, so you no doubt know the best thing to do and that's fine - just post your option. But..
...top marks go to the best explanation for your decision to open Door No............
Always switch. You have 2/3 chance of winning if you switch. If you stick with your first choice, your chance of winning remains at 1/3, the same as it was when you selected it. Think of it this way. After you have chosen the first time, your door has a 1/3 chance of winning. The other two doors, combined, have a 2/3 chance of containing the car. Removing one of those doors effectively "compresses" that 2/3 probability into the other door. So switch!
(This game (The Monty Hall game) depends on the host knowing which door contains the car, and always purposefully choosing a goat-door. Obviously, if the host opens a door at random, they will sometimes reveal the car. It changes the premise of the problem a bit, but whenever the host-opened door reveals a goat, you should switch.)
winkyincanada posted:Don Atkinson posted: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 the TV. Ah...that's better. But Have I Got News For You 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.
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! What a night!
Now the final challenge begins. The lights dim and the cheers of the crowd die down. Ant & Dec show you three doors numbered 1, 2 and 3. They say that the Porsche is hidden behind one of the doors. You must choose which one. If you choose correctly you win the Porsche. If not, you win a goat. The tension mounts. The audience can't contain themselves: shouts begin..."door 1"..."no door 2"...etc. You hesitate. Ant urges you to make a choice. Finally you choose door number 3. A green light comes on over door 3. Oh no...did I choose wisely...
A hush comes over the theatre as Dec walks over to door number 1 and motions to open it. The atmosphere can be cut with a knife. Slowly, Dec opens door 1 to reveal a goat! Phew that was lucky. The crowd bursts into a relieved cheer. But soon Ant has gripped the handle of door 2 and the crowd go silent. You can hear a pin drop.
The tension is unbearable...
Suddenly Ant 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?
As I said, it's an old one, so you no doubt know the best thing to do and that's fine - just post your option. But..
...top marks go to the best explanation for your decision to open Door No............
Always switch. You have 2/3 chance of winning if you switch. If you stick with your first choice, your chance of winning remains at 1/3, the same as it was when you selected it. Think of it this way. After you have chosen the first time, your door has a 1/3 chance of winning. The other two doors, combined, have a 2/3 chance of containing the car. Removing one of those doors effectively "compresses" that 2/3 probability into the other door. So switch!
(This game (The Monty Hall game) depends on the host knowing which door contains the car, and always purposefully choosing a goat-door. Obviously, if the host opens a door at random, they will sometimes reveal the car. It changes the premise of the problem a bit, but whenever the host-opened door reveals a goat, you should switch.)
However, when you make that second choice the odds at that point are 1/2 not 1/3 because one has been eliminated, so it is just a toss up: why change? So the question is simply, will you have the courage of your convictions, or swap? However if you don’t switch and don’t win you will kick yourself all the more for having chosen wrong twice, so maybe that is a reason for change, if a bad one - it is an evil thing to offer you just for greater entertainment. But then, that is what game shows are about!
if it was me I’d think the presenter is trying to save the cost of the Porsche (ok, the motorised goat) and tempting me to think that I should have chosen door 2.
sjbabbey posted:Door 2 on the basis that they’d want to keep the goats apart to prevent them fighting.
Nice one sjb. Correct answer and one of the more amusing explanations that I've ever heard.
Innocent Bystander posted:winkyincanada posted:Don Atkinson posted: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 the TV. Ah...that's better. But Have I Got News For You 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.
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! What a night!
Now the final challenge begins. The lights dim and the cheers of the crowd die down. Ant & Dec show you three doors numbered 1, 2 and 3. They say that the Porsche is hidden behind one of the doors. You must choose which one. If you choose correctly you win the Porsche. If not, you win a goat. The tension mounts. The audience can't contain themselves: shouts begin..."door 1"..."no door 2"...etc. You hesitate. Ant urges you to make a choice. Finally you choose door number 3. A green light comes on over door 3. Oh no...did I choose wisely...
A hush comes over the theatre as Dec walks over to door number 1 and motions to open it. The atmosphere can be cut with a knife. Slowly, Dec opens door 1 to reveal a goat! Phew that was lucky. The crowd bursts into a relieved cheer. But soon Ant has gripped the handle of door 2 and the crowd go silent. You can hear a pin drop.
The tension is unbearable...
Suddenly Ant 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?
As I said, it's an old one, so you no doubt know the best thing to do and that's fine - just post your option. But..
...top marks go to the best explanation for your decision to open Door No............
Always switch. You have 2/3 chance of winning if you switch. If you stick with your first choice, your chance of winning remains at 1/3, the same as it was when you selected it. Think of it this way. After you have chosen the first time, your door has a 1/3 chance of winning. The other two doors, combined, have a 2/3 chance of containing the car. Removing one of those doors effectively "compresses" that 2/3 probability into the other door. So switch!
(This game (The Monty Hall game) depends on the host knowing which door contains the car, and always purposefully choosing a goat-door. Obviously, if the host opens a door at random, they will sometimes reveal the car. It changes the premise of the problem a bit, but whenever the host-opened door reveals a goat, you should switch.)
However, when you make that second choice the odds at that point are 1/2 not 1/3 because one has been eliminated, so it is just a toss up: why change? So the question is simply, will you have the courage of your convictions, or swap? However if you don’t switch and don’t win you will kick yourself all the more for having chosen wrong twice, so maybe that is a reason for change, if a bad one - it is an evil thing to offer you just for greater entertainment. But then, that is what game shows are about!
if it was me I’d think the presenter is trying to save the cost of the Porsche (ok, the motorised goat) and tempting me to think that I should have chosen door 2.
Hi IB,
There's no easy way of putting this, so I'll just come clean.
You're wrong.
However, when this puzzle was first published (donkeys years ago !) even well-respected professors of mathematics at well-respected universities got it wrong. And argued like hell that they were right.
Monty Hall stopped the show once they realised that contestants realised that to "swap" was the best strategy.
PS, I like the "motorised goat" ..... I had thought of putting bicycles behind the doors rather than goats, but concluded that winky and one or two others would then "refuse" to try to win the Porsche and insist on sticking with their first choice in order to improve their chance of winning a bike
Innocent Bystander posted:Please can someone explain how the choice of switch or stick when the third choice has already been removed from the equation is 2/3. I’d like to see the statistical reasoning for it.
what if the presenter had go e to door 3 instead of door 2 once the goar had been revealed behind door 1?
This is the point of the puzzle............figuring out the explanation
You now have the "advantage" of knowing the correct answer, it's just the explanation that is missing
Remember, there is no certainty that "switching" will result in a win, it's just that the chances are 2/3 if you do "switch", whereas the chance is only 1/3 if you don't.