Can a monkey outrun a bullet and still save her litter?

[Georgepowell]

Another puzzle here:

You have the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9. Create two integers from these digits so that when you take one from the other you get 33,333.

eg.
12,345-6,789 = 5,556

As an extra challenge:

After you have found the solution(s), prove that they are the only solution(s).

 

[davee123]

You have the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9. Create two integers from these digits so that when you take one from the other you get 33,333.

Spoiler

41,268 - 7,935 = 33,333
41,286 - 7,953 = 33,333

After you have found the solution(s), prove that they are the only solution(s).

Hmmm...

DaveE

 

[Georgepowell]

Those were the solutions I got. And they ARE the only solutions.

I have proved it using funny diagrams and logic, but I can't draw these diagrams and show my proof formally on this site.

The basic idea of the proof (don't read if you want the complete challenge for yourself):

First you need to prove that all solutions involve a 5 digit number and a 4 digit number. This is easy.

Then you prove that the 5 digit number starts in either 3 or 4. (easy)

Then you assume that the first number is 3, then show that there is no possible solutions with the first digit being 3. This is slightly longer, but still easy.

Then I drew a table of all the possible pairs of number that their difference is 3 or 4, and grouped them into four groups:
(4,X). remainder four, the first number in the pair is the larger one. i.e. (9 - 5)
(4,Y). remainder four, the first number is smaller. i.e. (3 - 9)
(3,X). remainder three, first is larger. i.e. (9 - 6)
(3,Y). remainder three, first is smaller. i.e. (2 - 9)

You need to pick four pairs that do not repeat a digit and do not include zero or 4 (because this is the first digit of the 5 digit number).

http://i349.photobucket.com/albums/q390/Georgepowell77/DSC00137.jpg

That is an image of my basic idea.

There are now 8 situations that could lead to a solution. I went through each one and proved that 7 of them could not yeild a solution (I did this by using weird clock-like diagrams).

Then there is one combination of group choices that could lead to a solution. and it is very easy to show that there are only two combinations of pairs from these groups that leads to a solution. And they are the solutions that we got.

 

[xbisphambabex]

NOt right;
Can anyone answer this?
2) A murderer is condemned to death. He has to choose between three rooms: The first is full of raging fires, the second is full of assassins with loaded guns, and the third is full of lions that haven't eaten in 3 years. Which room is safest for him?

the third room is the safest to choose as the lions would be dead if they hadnt eaten for 3 years

 

[Georgepowell]

Joe has been showing Penny a few optical experiments. In one experiment he placed six mirrors vertically to form a regular hexagon with small gaps between the mirrors. Through one gap he shone a laser beam so it emerged straight from the gap diametrically opposite.

Penny then had to work out the smallest angle through which the beam must be rotated so that it emerged from the same gap as before, after being reflected just once by all six mirrors.

What was that small angle (rounded to the nearest degree)?

 

[DaveC426913]

Joe has been showing Penny a few optical experiments. In one experiment he placed six mirrors vertically to form a regular hexagon with small gaps between the mirrors. Through one gap he shone a laser beam so it emerged straight from the gap diametrically opposite.

Penny then had to work out the smallest angle through which the beam must be rotated so that it emerged from the same gap as before, after being reflected just once by all six mirrors.

What was that small angle (rounded to the nearest degree)?

Upon what axis is the beam rotated? I presume the rotation axis can't be in line with the centre of the hexagon (i.e. spin the mirror contraption rather than the laser), so the axis of rotation must be the point where the laser beam first enters the hexagon?

 

[Georgepowell]

Upon what axis is the beam rotated? I presume the rotation axis can't be in line with the centre of the hexagon (i.e. spin the mirror contraption rather than the laser), so the axis of rotation must be the point where the laser beam first enters the hexagon?

It is rotated about the point where it first enters the hexagon.

 

[DaveC426913]

I don't do answers. But I like diagramming questions!

 

[Georgepowell]

So is my question too difficult for the genius's of PhysicsForums.com ?

 

[Rogerio]

Joe has been showing Penny a few optical experiments. In one experiment he placed six mirrors vertically to form a regular hexagon with small gaps between the mirrors. Through one gap he shone a laser beam so it emerged straight from the gap diametrically opposite.

Penny then had to work out the smallest angle through which the beam must be rotated so that it emerged from the same gap as before, after being reflected just once by all six mirrors.

What was that small angle (rounded to the nearest degree)?

Spoiler

9 degrees.
In fact, atan(sqrt(3)/11).

 

[roam]

It is given that there are two sets of real numbers A={a₁, a₂,..., a₁₀₀} and B={b₁, b₂,..., b₅₀}. If there is a mapping f from A to B such that every element in B has an inverse image and

f(a₁) ≤ f(a₂) ≤...≤ f(a₁₀₀)

Then the number of such mapping is...

A) C⁵⁰₁₀₀

B) C⁵⁰₉₉

C) C⁴⁹₅₀

D) C⁴⁹₉₉

 

[Georgepowell]

Spoiler

9 degrees.
In fact, atan(sqrt(3)/11).

why? what was your logic?

 

[Rogerio]

why? what was your logic?

I hope it is enough.

 

[DaveC426913]

I hope it is enough.

Wow. What a brilliant way of solving it.

 

[redargon]

I don't get it?

 

[roam]

The answer is (D): C⁴⁹₉₉

 

[cool_arrow]

Hi everyone. I saw this problem in a logic textbook I had in a class many years ago:

Two friends meet after having been out of contact with one another for some
years. They have the the following conversation:

A: I have three sons.
B: What are their ages?
A: The product of their ages is 36.
B: That is not enough information.
A: The sum of their ages is the same as the the number on the building across the street.
B: Give me a minute to work it out with pencil and paper.

B: I've almost got it but I need one more clue.
A: The oldest one has red hair.
B: I've got it.

What are the ages of the three sons?

 

[Rogerio]

Hi everyone. I saw this problem in a logic textbook I had in a class many years ago:

Two friends meet after having been out of contact with one another for some
years. They have the the following conversation:

A: I have three sons.
B: What are their ages?
A: The product of their ages is 36.
B: That is not enough information.
A: The sum of their ages is the same as the the number on the building across the street.
B: Give me a minute to work it out with pencil and paper.

B: I've almost got it but I need one more clue.
A: The oldest one has red hair.
B: I've got it.

What are the ages of the three sons?

Well, it is a classic puzzle, and I've seen it a couple of times, right in this forum...

https://www.physicsforums.com/showthread.php?t=50813"

 

[Rogerio]

Wow...

Thanks, Dave!

 

[redargon]

Thanks, Dave!

I still don't get it, could you explain your diagram a little please?

 

[Rogerio]

I still don't get it, could you explain your diagram a little please?

Just try to follow the ray, using geometry.

The figure shows the first reflection.
Note the first mirror surface (blue line) , its normal (yellow line) , the reflected ray (pink line) , and the simmetrical points (cyan).

After the first reflection you have to follow the pink line. However, everything goes as you were at the second hexagon following the red line, and so on.

Just follow the ray, and you'll understand!

 

[DaveC426913]

Just try to follow the ray, using geometry.

The figure shows the first reflection.
Note the first mirror surface (blue line) , its normal (yellow line) , the reflected ray (pink line) , and the simmetrical points (cyan).

After the first reflection you have to follow the pink line. However, everything goes as you were at the second hexagon following the red line, and so on.

Just follow the ray, and you'll understand!

There's a puzzle out there that involves figuring out how long a diagonal line you can draw on a cylinder (a toilet paper roll). It's easily resolved by unrolling the toilet paper into its "net" and drawing a straight line across it. I haven't been able to find it.

The closest I've come is the fly-on-a-wall problem, here called Sneaking Spider:
http://www.puzzle.dse.nl/math/index_us.html#sneaking_spider

The trick is that you can lay the surfaces out in a way that allows for much easier geometry. In the laser&mirror problem, you're doing the same thing.

 

[Jannes20]

NOt right;
Can anyone answer this?
2) A murderer is condemned to death. He has to choose between three rooms: The first is full of raging fires, the second is full of assassins with loaded guns, and the third is full of lions that haven't eaten in 3 years. Which room is safest for him?

The lions that haven't eaten for 3 years duhh they are DEAD!

 

[DaveC426913]

The lions that haven't eaten for 3 years duhh they are DEAD!

for a riddle posed 4 months and 8 days ago...
you are 4 months, 7 days and 22 hours late - it was answered within 2 hours.

 

[guusebumps]

Exactly how many slices of 1.5 cm each can you cut from a whole bread which is 22.5 cm long?

The key is the word WHOLE BREAD.

So you can cut only 1 slice, and then the bread is no longer a WHOLE BREAD.

 

[mvp112]

1) A detective was called on a murder scene at 3:00 in the morning .. he found the dead body lying on the sidewalk .. he took the phone of the deceased and dialed the last called number .. his brother answers the call .. the detective said " Your brother is dead quickly come to the spot " .. his brother quickly turned up to the crime scene and the detective arrested him ...
Why did the detective arrested him ?





(i am not an English speaker so there might be mistakes, just ignore them)

 

[mvp112]

2) A mother of two sisters died, at her funeral one sister saw a men and fell in love with him , but he ignored and left . She was disappointed and wanted to see him again , but there was no sign of him , she searched her entire family but he was no where to be found . Other sister says that you won't find him , the first says yes i will and stabs the other sister and she finally found her man ... HOW ??(i am not an English speaker so there might be mistakes, just ignore them)

 

[Sorry!]

1) A detective was called on a murder scene at 3:00 in the morning .. he found the dead body lying on the sidewalk .. he took the phone of the deceased and dialed the last called number .. his brother answers the call .. the detective said " Your brother is dead quickly come to the spot " .. his brother quickly turned up to the crime scene and the detective arrested him ...
Why did the detective arrested him ?





(i am not an English speaker so there might be mistakes, just ignore them)

cause he knew where 'the spot' was. lol stupid brother.

 

[DaveC426913]

2) A mother of two sisters died, at her funeral one sister saw a men and fell in love with him , but he ignored and left . She was disappointed and wanted to see him again , but there was no sign of him , she searched her entire family but he was no where to be found . Other sister says that you won't find him , the first says yes i will and stabs the other sister and she finally found her man ... HOW ??

Spoiler

He shows up at her funeral.

 

[binani777]

Hei guys I'm new to the thread.

I got a mind boggling one for you. (at least i think so)

Tom and an elderly lady got on bus number 56. There are no seats available and both of them have to stand on the bus. Tom reaches up and holds on to the overhead bar for stability.

The elderly lady is unable to reach the overhead bar to stabilize herself thus she reaches out and pinches Tom on his forearm, using it as a handhold.

What can Tom do to make the elderly person let go of his hand, without making it obvious to her that he doesn't want her pinching his arm?

There is going to be tonnes of answers i expect. But only one solution is the most elegant. (a matter of opinion)

 

[davee123]

What can Tom do to make the elderly person let go of his hand, without making it obvious to her that he doesn't want her pinching his arm?

1) Fall over
2) Pinch her arm
3) Wipe his snotty nose all over his opposing sleeve
4) Pretend to have minor muscle spasms
5) Put his arm around her as if to come on to her
6) Sit down on the floor
7) Start singing an aria, getting progressively louder
8) Etc.

DaveE

 

[Jimmy Snyder]

Tell her "This is the 57 bus, mom."

 

[binani777]

well not too much activity here eh.

here is my answer. better if you re-enact the scene on the bus with someone. (i.e. you are tom and your friend, the old lady)

Old lady: pinches Tom's forearm.
Tom: pinches the other side of his forearm.
Old lady:loses grip on Tom's forearm.

 

[gtatix]

2) A mother of two sisters died, at her funeral one sister saw a man and fell in love with him , but he ignored and left . She was disappointed and wanted to see him again , but there was no sign of him , she searched her entire family but he was no where to be found . Other sister says that you won't find him , the first says yes i will and stabs the other sister and she finally found her man ... HOW ??



(i am not an English speaker so there might be mistakes, just ignore them)[/QUOTE]

Believing that because the man showed up to her mother's funeral the sister who fell in love with the man was a sick psycho-sociopath. She concluded - in her sick mind - that the man had to have paid respects to the mother so by knowing the family - he would show up to a funeral of the mother's family if there were another death. She kills her sister to create a funeral that the man would attend!

 

[gtatix]

Methodical solution required:

You have a thick glass wine bottle that is empty. You have the original cork that was in the bottle. The cork is completely intact and there are no cracks or holes in the bottle - this is NOT a trick question.

Someone forces the cork - and it is very hard to push in with their thumb so they actually may need a blunt object like the heel of a knife - completely into the bottle.

The cork can be seen bouncing around inside the bottle if it is shaken or moved.

How can you get the cork out of the bottle without breaking the bottle or damaging - i.e. cutting or mutilating - the cork?

I have done this in bars and restaurants. In one Chinese buffet restaurant, I showed some of the staff and they couldn't believe it! They ran around telling all their fellow staff members showing them how to do it. They even gave me a green tea gift set!

 

[Jimmy Snyder]

How can you get the cork out of the bottle without breaking the bottle or damaging - i.e. cutting or mutilating - the cork?

Spoiler

Fill the bottle with water and freeze it.

 

[coverme]

NOt right;
Can anyone answer this?
2) A murderer is condemned to death. He has to choose between three rooms: The first is full of raging fires, the second is full of assassins with loaded guns, and the third is full of lions that haven't eaten in 3 years. Which room is safest for him?

the third becaus elion not eating for 3years are dead

 

[gtatix]

Spoiler

Fill the bottle with water and freeze it.

Jimmy, I don't know if I could disprove this but I would suggest that this may not force the cork to exit.

Lets add that you want the cork out now - within 5 minutes - and we don't have any "exotic" liquid gasses or such around!

I'm trying to respond without alluding to your answer thus ruining it for others who don't want to peek at the "spoiler."

 

[gtatix]

Awe inspiring physics/bar trick:

There are a number of ways this could be asked, but the principle is the same. I traded this puzzle/answer for the wine bottle/cork puzzle many years ago!

This is a practical puzzle that can be performed for visual effect - much the same as the wine bottle puzzle.

There is a plate - say 8" to 10" in diameter. It has a slightly curved edge so you could poor perhaps a couple of cups of water into it and the water would measure about 1/4" deep in the middle. The plate is "filled" with water so that it is about 1/2" from the rim all the way around.

The plate is set on a level table or desktop. Approximately 2" from the inside edge of the plate is a quarter. It is thus submerged. You have a "rock glass" or similar - not too thick of a rim and about 2" in diameter at the entrance. The glass is around 5" tall. You have a seedless - Maraschino cherry. You have a pack of matches.

You cannot move the plate. You cannot tip it or slide it etc. You can use any of - and only - the items given. You cannot push or splash - or the likes - the water from the plate. You must get access to the quarter and get it off of the plate with ONLY your finger without putting your finger into the water - basically without getting your finger wet - other than for the fact that the quarter may be a little damp or have a few drops of water on it.

How can you do this? I know of only one way and it is demostratable, not in any way a bizarre notion like waiting for a hurricane etc. etc. etc.

 

[Andre]

Methodical solution required:
How can you get the cork out of the bottle without breaking the bottle or damaging - i.e. cutting or mutilating - the cork?

Spoiler

http://www.metacafe.com/watch/455316/the_cork_out_of_the_bottle_trick/

 

[TheStatutoryApe]

Spoiler

http://www.metacafe.com/watch/455316/the_cork_out_of_the_bottle_trick/

Ah... nice.
I was thinking the same sort of idea but...

Spoiler

using a napkin

I'm not sure my idea would work so well.

 

[DaveC426913]

Awe inspiring physics/bar trick:

There are a number of ways this could be asked, but the principle is the same. I traded this puzzle/answer for the wine bottle/cork puzzle many years ago!

This is a practical puzzle that can be performed for visual effect - much the same as the wine bottle puzzle.

There is a plate - say 8" to 10" in diameter. It has a slightly curved edge so you could poor perhaps a couple of cups of water into it and the water would measure about 1/4" deep in the middle. The plate is "filled" with water so that it is about 1/2" from the rim all the way around.

The plate is set on a level table or desktop. Approximately 2" from the inside edge of the plate is a quarter. It is thus submerged. You have a "rock glass" or similar - not too thick of a rim and about 2" in diameter at the entrance. The glass is around 5" tall. You have a seedless - Maraschino cherry. You have a pack of matches.

You cannot move the plate. You cannot tip it or slide it etc. You can use any of - and only - the items given. You cannot push or splash - or the likes - the water from the plate. You must get access to the quarter and get it off of the plate with ONLY your finger without putting your finger into the water - basically without getting your finger wet - other than for the fact that the quarter may be a little damp or have a few drops of water on it.

How can you do this? I know of only one way and it is demostratable, not in any way a bizarre notion like waiting for a hurricane etc. etc. etc.

Presumably, there are some conditions missing. Either that, or you're going to get your butt kicked if there's any money riding on this.

At it stands, there is nothing preventing me from using glass, match or cherry to simply push the quarter to the edge of the plate and off into my hand.


Anyway, here's my solution:

Spoiler

Light match, stick in cherry.
Put cherry and match on plate next to quarter.
Drop glass over top of match/cherry and quarter.
Heated air will force water out from under glass, till quarter is dry.
Pull glass/quarter over to edge of plate. Quarter will fall off into your hand.

 

[gtatix]

Ah... nice.
I was thinking the same sort of idea but...

Spoiler

using a napkin

I'm not sure my idea would work so well.

Your idea is the way I was taught. It is tough because it has to be thin but tough.

 

[gtatix]

Presumably, there are some conditions missing. Either that, or you're going to get your butt kicked if there's any money riding on this.

At it stands, there is nothing preventing me from using glass, match or cherry to simply push the quarter to the edge of the plate and off into my hand.


Anyway, here's my solution:

Spoiler

Light match, stick in cherry.
Put cherry and match on plate next to quarter.
Drop glass over top of match/cherry and quarter.
Heated air will force water out from under glass, till quarter is dry.
Pull glass/quarter over to edge of plate. Quarter will fall off into your hand.

Dave, I did include this: "You must get access to the quarter and get it off of the plate with ONLY your finger without putting your finger into the water." Maybe the wording is a bit ambiguous but I meant that accessing - basically touching the quarter at all - can only be done with the finger.

That said, you basically have solved it except that what will happen is

Spoiler

you need to put the cherry in the centre of the plate so the glass can go over the cherry and burning match but leaving the quarter on the outside of the apparatus where it is - away from the centre near the edge. The water will actually rise inside the glass due to the fact that the air inside will be used up to fuel the fire creating a vacuum causing the water to be sucked up and inside! The water rises and uncovers the quarter thus allowing access. You should try this because the visual - especially to non-science folk - is virtually magical!

 

[DaveC426913]

Dave, I did include this: "You must get access to the quarter and get it off of the plate with ONLY your finger without putting your finger into the water." Maybe the wording is a bit ambiguous but I meant that accessing - basically touching the quarter at all - can only be done with the finger.

That said, you basically have solved it except that what will happen is

Spoiler

you need to put the cherry in the centre of the plate so the glass can go over the cherry and burning match but leaving the quarter on the outside of the apparatus where it is - away from the centre near the edge. The water will actually rise inside the glass due to the fact that the air inside will be used up to fuel the fire creating a vacuum causing the water to be sucked up and inside! The water rises and uncovers the quarter thus allowing access. You should try this because the visual - especially to non-science folk - is virtually magical!

Right. Cool.

 

[Capt. McCoy]

verty's right...it just said there are no doors...not no doorways...

 

[Capt. McCoy]

The judge is the father of the son of the criminal...How is the judge and the criminal related?

 

[Jimmy Snyder]

The judge is the father of the son of the criminal...How is the judge and the criminal related?

Poor brain teaser.

Spoiler

If the criminal is a man, then the judge is the criminal. Otherwise, the criminal could be any woman, relative or not.

 

[seshuprakash]

NOt right;
Can anyone answer this?
2) A murderer is condemned to death. He has to choose between three rooms: The first is full of raging fires, the second is full of assassins with loaded guns, and the third is full of lions that haven't eaten in 3 years. Which room is safest for him?

the 3rd room is safest room , becoz of the lions were dead due to they doesn't eaten ny thing since 3 yrs.

 

[seshuprakash]

3)(in your head!) Take 1000 and add 40 to it. Now add another 1000. Now add 30. Add another 1000. Now add 20. Now add another 1000. Now add 10. What is the total?
pls sincerely add it in mind...

4100 hahahalol