Puzzle Corner

[northcat_8]

"Fairground Worker"

The main merry-go-round at a fairground needs a fresh lick of paint on the decking that people walk on. This decking is effectively a larger circle with a smaller concentric circle cut out (see diagram).

A fairground worker is given a ball of string and told that by using the string as in the diagram - a straight line from one edge of the circle, just touching the edge of the "hole" and over to the other side - he can figure out how much paint is needed to repaint the decking for the merry-go-round.

How is this done?

I'm not going to answer this one...being a math teacher is cheating a little on this one...but I will offer some facts.

#1 - a segment tangent to a circle is perpendicular to a radius of the circle at the point of tangency.
#2 - If 2 circles are concentric and a chord of the outer circle is tangent to the inner circle, then the point of tangency is the midpoint of the chord


There are about 100 different ways to solve this problem depending on the depth of your mathematical understanding. Good question.

[northcat_8]

Another easy one:

Jim is out hunting. Walking through the woods he was suprised by a huge bear about 100 yards due east of him. In a panic Jim ran, not directly away from the bear, but in his haste ran due north. After running about 100 yards, he had regained control, stopped, turned and shot due south and killed the bear; who had not moved from it's original position.

What color was the bear?

[thecoalman]

White it's a polar bear. If the bear was due east and he ran north then shot south......and the bear never moved

[tgpo]

What's next?

[Devanshu]

2 6s back to back. Dont you just love the simpsons?

Great thread by the way.

EDIT: Here's mine...

A farmer and his sons are carrying grain sacks to the barn at the end of a day. The farmer is carrying one sack of grain and his sons are carrying two sacks. Who is carrying the heavier sack?

[northcat_8]

Not a riddle but a point to ponder....

The definition of a island is "a body of land completely surrounded by water"
The definition of a lake is "a body of water completely surrounded by land"

So my question is:
Suppose the northern hemisphere were all land and the southern hemisphere were all water...would you call the northern hemisphere an island or the southern hemisphere a lake?

[flaninacupboard]

neither, land would be land and sea would be sea. no further defintion would be neccesary. i don't know where all the rain would be going if there were no rivers though, perhaps it only rains in the southern hemisphere too? :P

[northcat_8]

Not quite so easy....

Consider this....

[northcat_8]

One more before I get to work editing some video.......

A strange man comes to town and asks the barber if he had any competition. The barber says "No, none at all. Of all the men in town, I obviously do not shave those who shave themselves , but I do shave all those who don't shave themselves."

Question: Who shaves the barber?

[northcat_8]

OK...one more, but this one is not really a Q and A type of thing...but interesting....

Take any 3 digit number, whose first and last digits have a difference greater than 1. Now form a 2nd number by reversing the digits.

Example:
1st # = 742
2nd # = 247

Step 1 - Now subtract the smaller number from the larger...742-247=495
Step 2 - Take the result (495) and add the reverse of it (594)....495+594 = 1089

The result is always 1089 ...try it yourself... 8)

[flaninacupboard]

One more before I get to work editing some video.......

A strange man comes to town and asks the barber if he had any competition. The barber says "No, none at all. Of all the men in town, I obviously do not shave those who shave themselves , but I do shave all those who don't shave themselves."

Question: Who shaves the barber?

The barber doesn't live in town 8)

[Ironballs]

The barber is a woman

[northcat_8]

Ah...break time....

Actually the situation with the barber is a paradox and is without an answer, unless the barber is a woman, but "barber" is masculine and generally accepted to be male. But the barber being a woman would satisfy the conditions. There is no reference to where anyone lives, only that they are currently "in the town".

Like the couple of posts about God and the Rock. If God is all powerful...then obviously he can make a rock as large as he wants or needs too...but being all powerful that rock would never be big enough that he could not move it....hence the paradox.

[gll99]

Three very smart friends in a foreign land are caught stealing palace jewels and they are brought before the king for punishment. The king says that he will perform a test to see what their sentence will be. He tells them that he has 3 white hats and two black hats. He will place one hat upon each of their heads and they will stand in a row being able only to see the hat of the one(s) in front of them. The first one will only see a wall, the second one will see the hat color of the first guy and the third will see the hats of the two in front of him.
They have one hour to respond. If any one of them can say the color of his own hat all 3 will go free. If none can say then they will be imprisonned for 15 years. If they try to guess and cannot explain their reason or if they say the wrong color they will be beheaded.

Just when the hour is almost up the guy closest to the wall who cannot see any hats says that his hat is white and provides the explanation. They all go free.

What was is reasoning?

[northcat_8]

Sorry, I PM'd the question.

[gll99]

extra info due to pm:

No one will poll these guys for their opinion and they only have one hour.
They can't move, make signs, peek or say anything at all except their hat color. They must stand in a straight line facing the wall. Only one guy can speak when he thinks he knows the answer and say his hat color and it ends there there is no second chance. If anyone says anything else it's the very short hair cut treatment and the head goes with it.

This is totally logical. There are no tricks, no mirrors and no snitches. Although I show certain color hats only the first guy has a white hat for sure but the other two could be either white or black. It will not affect the logic.

p.s. If your concerned about them knowing the time then assume that there is a clock on the wall that they can all see. It doesn't factor into the puzzle other than the fact they must speak and be right before the hour is up or get 15 years in jail.

[gll99]

Similar to the door one asked earlier.

I land on a large island and want to reach the only town on the other side of the island. I come to a fork in the road but no markings indicate which way leads to town. I see a native standing there at the fork. I know that only 2 types of natives live on this island. Those who always lie and those who always tell the truth. I don't know to which group this native belongs. How do I find out which path will get me to town. The other way will lead deep into the jungle and night is approaching.

[daamon]

Daamon almost had it, he just had to connect them correctly.

Ah, bugger. So easy when you know the answer...

[daamon]

@ thecoalman - "Thumbs 'n' Pencil" puzzle:

OK, here goes:

1. Start as described with hands in a "praying" position, thumbs pointing upwards, and fingers pointing away from the body (not skywards).
2. Twist your hands in opposite directions, e.g. the right hand upwards, and the left hand downwards, rotating around a line through the palms of your hands (a horizontal line, left to right).
3. At the same time, rotatate the pair of hands clockwise (if right hand is going upwards) about a line that runs vertically so that, half way through the manoevure, your fingers are pointing in opposite directions and the back of one of your hands (depends which way you rotated - left or right handed) is facing you. One thumb is pointing up, the other down.
4. Continue the move until your hands end up the same as when they started, but with the thumbs pointing downwards and your arms crossed at the wrist.
5. Now move your the palms of your hands apart to grip the pencil...

[daamon]

Not quite so easy....

Consider this....

Clever, I like it. I'll PM you northcat so that others can ponder it awhile...

[gll99]

Very old but some may not know this one.

Jimmy was very happy to finally spend time with the father he had not seen in over 40 years but as luck would have it they were involved in a serious car accident and his father was killed instantly. Jimmy was seriously hurt and needed emergency surgery. Fortunately for him old Doc Brown a renowned surgeon was on duty at the hospital that night. However when Jimmy was brought in Doctor Brown exclaimed I can't operate on that man he's my son!

How could this be?

[Tommyknocker]

Very old but some may not know this one.

Jimmy was very happy to finally spend time with the father he had not seen in over 40 years but as luck would have it they were involved in a serious car accident and his father was killed instantly. Jimmy was seriously hurt and needed emergency surgery. Fortunately for him old Doc Brown a renowned surgeon was on duty at the hospital that night. However when Jimmy was brought in Doctor Brown exclaimed I can't operate on that man he's my son!

How could this be?

Old Doc Brown doesn't have any "Y" chromosomes.

[gll99]

Tommyknocker
very good. With the quick answer I guess you knew that one.

Want to try the fork in the road one or the b/w hats?

[Tommyknocker]

Tommyknocker
very good. With the quick answer I guess you knew that one.

Want to try the fork in the road one or the b/w hats?

Pick your favorite native and ask "If I ask the other native which road leads to town, what will he say?'

What ever direction the native you are speaking to points, just go the other way.

[gll99]

Pick your favorite native and ask "If I ask the other native which road leads to town, what will he say?'

There's only one native at the fork in the road. No one else is in sight.

edited in:

btw even if there was another native that won't work in this case.

[Ironballs]

Not quite so easy....

Consider this....

Clever, I like it. I'll PM you northcat so that others can ponder it awhile...

You are mixing two units of currency, so the first equation is not valid.

[thecoalman]

Daamon,

Not sure if you got it right but here's two images to explain it better. You start with the pencil on top and it has to end up on the bottom. At no times does the pencil leave the crooks of either of your hands. You can do it backwards too but it's probably harder to learn it that way.

I could make a short vid, no camera here tho.

[daamon]

Clever, I like it. I'll PM you northcat so that others can ponder it awhile...

You are mixing two units of currency, so the first equation is not valid.

I'll leave northcat_8 to comment, as he posed the problem (and maths is "my thing"). But my answer was different, so only one of us (or neither) is right!

[daamon]

Daamon,

Not sure if you got it right...

Not quite, my hands end up with everything OK except that my thumbs are apart rather than together (as per your 2nd photo), and my arms crossed.

I'll keep trying...

Does in involve detaching a false arm at any point..?

[thecoalman]

Does in involve detaching a false arm at any point..?

Nope no false arm. I've done it in front of people even slowly and they still can't do it. I'll give you a hint. The ends of the pencil end up opposite of how they start.

I'll post a pic by pic example of how to do it if you want.