34
   

The worlds first riddle!

 
 
markr
 
  1  
Reply Sat 30 Jul, 2005 04:30 pm
Try: Some of your patterns are disconnected, and the second won't work. I think you have some alignment problems.
0 Replies
 
Tryagain
 
  1  
Reply Sun 31 Jul, 2005 06:13 am
Mark wrote, "Try: Some of your patterns are disconnected, and the second won't work." Shocked

Quite right, they did not look like that earlier. However, all now appears well. If you can come up with another shape, I shall be delighted to hear from you.

"I think you have some alignment problems."

Schoosh! Don't tell Rap. Drunk
0 Replies
 
Tryagain
 
  1  
Reply Sun 31 Jul, 2005 11:04 am
Rap:

Average
n=5*6-4*7=28 (8 too many)

Camera
Serial Number 2835 Cool

Bananas
n=m*5*6=m*30
30mod7=2 group 2,4,6,1,3,5,0 m=4
m*20=130
120 bananas Cool

Perfect Square
n=10,100=100^2
so for n<100 there's 99 unless 0^2 is included, then it's 100 Cool Cool


Mark:
FIVE NUMBERS
2 Cool

SERIAL NUMBER
2835 Cool

BANANAS
120 Cool

SQUARES
99 Cool




A2K has 20 new offices that each need to have a number placed on the door. The office manager will purchase metal numerals and nail them to the doors. The cost of the numerals varies depending on the digit:

1 = 1 Kwanza
2 = 2 Kwanzas etc.
0 = 10 Kwanzas

So, for example, putting the number 6 on a door would cost 6 Kwanzas. The number 13 would cost 4 Kwanzas. The number 10 would cost 11 Kwanzas.

The only requirement is that the numbers be in consecutive order. What is the least expensive way to do the job Question


Mark, Rap and Zippy rode their bicycles to school. Each had a chain and a lock. Mark locked his bike to a lamppost and to Rap's bike. Rap locked his bike to the lamppost and also to Zippy's bike. Zippy locked his bike to the lamppost and to both Mark and Rap's bikes. Each bike was now held by two locks.

Later that day Mark lost his key! Embarrassed With the two keys they had left, they could unlock only one of the bicycles. Whose bicycle was it Question
0 Replies
 
markr
 
  1  
Reply Sun 31 Jul, 2005 02:38 pm
[size=7]OFFICE NUMBERS
1-20 is $122. Starting with a higher number will cost more.
Substituting 6 for 9 lowers the cost to $116.

BICYCLES
Zippy's
[/size]
0 Replies
 
raprap
 
  1  
Reply Sun 31 Jul, 2005 05:51 pm
Door Numbers

[size=7]Simplest way is to number them from 1 to 30

C=$2*10*9/2+11*$1+2*$10=$90+$11+$20=$121
But if the inverse of a 6 becomes a 9I'd mind cause I could save the company $6, and the cost would be $115[/size]


Bike Locks

[size=7]Mark's chain locked to Rap, Lamppost, Mark
Rap's chained to Zippy, Lamppost, Rap
Zippy's chained to Mark, Rap, Lamppost, Zippy

Rap has three locks and chains, Rap needs all locks to be open. So Rap is not free if Mark doesn't unlock. Mark's bike is locked by Mark so Mark's Bike doesn't unlock.

Supposition if any of the three unlocks it must be Zippy, Check Zippy has two locks, one locked by Zippy and the other to Rap,

Bingo?-Free at last, Free at last, Lord have Mercy, Zippy is free at last.[/size]


Rap c∫;?/
0 Replies
 
Tryagain
 
  1  
Reply Mon 1 Aug, 2005 07:39 am
Mark:

OFFICE NUMBERS
1-20 is $122. Starting with a higher number will cost more. (I make that $132)

Substituting 6 for 9 lowers the cost to $116. Cool

BICYCLES
Zippy's Cool

Rap:

Door Numbers

Simplest way is to number them from 1 to 30 (Is this the same as 1-20?)

C=$2*10*9/2+11*$1+2*$10=$90+$11+$20=$121
But if the inverse of a 6 becomes a 9I'd mind cause I could save the company $6, and the cost would be $115 Cool

Well, whatever. If the numbering starts with 0-19 a further $2 can be saved. :wink:

Bike Locks

Mark's chain locked to Rap, Lamppost, Mark
Rap's chained to Zippy, Lamppost, Rap
Zippy's chained to Mark, Rap, Lamppost, Zippy

Rap has three locks and chains, Rap needs all locks to be open. So Rap is not free if Mark doesn't unlock. Mark's bike is locked by Mark so Mark's Bike doesn't unlock.

Supposition if any of the three unlocks it must be Zippy, Check Zippy has two locks, one locked by Zippy and the other to Rap,

Bingo?-Free at last, Free at last, Lord have Mercy, Zippy is free at last. Cool



(The only important information is which bikes Mark's chain had locked up. What Zippy and Rap did is unnecessary information since in the end they removed their chains. Since Mark chained his bike to the lamppost and to Rap's bike, those two bikes remained tied up. Zippy's bike was free.)



Off the coast of Nue Joisey there is a flat, rocky island named Brighton, where only grass and lichen grow. The island is roughly 2 hectares (about 5 acres) in area.

On the island there is only one structure: a 75 meter tall stone lighthouse.
A tourist on the island wanted to visit the lighthouse and set off down the road. Shortly, he came to a four-way fork and didn't know which way to turn. But, as the tourist agency had told him in advance, he would find four island guides, each standing by one of the four roads. He could ask them for directions to the lighthouse.

Unfortunately, these people are not all truthful all the time.

One always tells the truth. Another always lies.

The third always responds truthfully to the first question asked, but after that will tell the truth if the previous question asked of any of the four was answered truthfully, but lie if the previous question was answered falsely.

The fourth person will always lie in response to the first question asked, but like the third person, respond to subsequent questions with the same honesty as the person who responded to the previous question the tourist posed.

What is the minimum number of questions you need to ask to find your way to lighthouse Question Twisted Evil



You have a cylindrical container just big enough to hold 3 tennis balls. Now you want to make a label for the container and you have to decide whether to wrap the label around the cylinder, or up the side. Which direction is longer Question



A9543B represents a six-digit number in which A and B are digits different from each other. The number is divisible by 11 and also by 8. What digit does A represent Question


The average of five numbers is 16. Suppose 10 is added to the five numbers. What is the average of the six numbers Question


The four-digit numeral 3AA1 is divisible by 9.What digit does A represent Question


A set of marbles can be divided in equal shares among 2, 3, 4, 5, or 6 children with no marbles left over. What is the least number of marbles that the set could have Question
0 Replies
 
markr
 
  1  
Reply Mon 1 Aug, 2005 09:06 am
LIGHTHOUSE
Interesting - I'll need to think about this one.

[size=7]TENNIS BALLS
Since pi > 3, ...

A9543B
7

SIX NUMBERS
15

3AA1
7

MARBLES
60
[/size]
0 Replies
 
markr
 
  1  
Reply Mon 1 Aug, 2005 01:45 pm
LIGHTHOUSE
I assume that questions are directed toward individuals, and therefore, persons three and four don't base their answers on the previous response until the second question that is directed their way.

The following method will take no more than five questions, but could take as few as two.

[size=7]Ask "Do you always tell the truth?" until you get a "no" response. Then ask this person which road leads to the lighthouse.

The only person who will answer "no" is person three. Since person three just told the truth, he will answer a follow-up question truthfully.
[/size]
I don't know if this is optimal.
0 Replies
 
markr
 
  1  
Reply Mon 1 Aug, 2005 02:03 pm
LIGHTHOUSE
Added assumption: they each are aware of the others' habits. This method always takes four questions.

[size=7]Pick one (call him A). Ask these three questions:
Does B always tell the truth?
Does C always tell the truth?
Does D always tell the truth?

Person one will answer with "no, no, no."
Persons two and four will answer (perhaps not in this order) with "no, yes, yes" where the "no" applies to person one.
Person three will answer (perhaps not in this order) with "yes, no, no" where the "yes" applies to person one.

If you get "no, no, no," then ask that same person which road to take.
If you get "no, yes, yes," then ask the person that the "no" applied to which road to take.
If you get "yes, no, no," then ask that same person or the person that the "yes" applied to which road to take.
[/size]
0 Replies
 
raprap
 
  1  
Reply Mon 1 Aug, 2005 09:42 pm
Rocky Island Guides

[size=7]I opine there are no more than four questions to get to the teller's of truth in all cases

I'll label the guides A,B,C&D.
A Lies
B is Truthful
C Starts with the Truth, then lies
D Starts with a Lie, then becomes Truthful

Start with three questions about the certifiable honestly of the others.

If A (BCD-NYY) (BDC)-NYY) (CBD-YNY) (CDB-YYN) (DBC-YNY) (DCB-YYN)
If B (ACD-NNN) (ADC_NNN) (CAD-NNN) (CDA_NNN) (DAC-NNN) (DCA-NNN)
If C (ABD-NNY) (ADB-NYN) (BAD-YYY) (DBA-NNY) (BAD-YYY) (BDA-YYY)
If D (ABC-YYN) (ACB-YNN) (BAC-NNN) (BCA-NNN) (CBA-YYN) (CAB-YNY)

If you get three N ask them. You've either got B or D in truth
If you get three Y you've got C as liar, so ask ?'Who never lies?', and he'll get you to B.
If you get two N's and a Y you've got C as liar, ask the same question to get B
If you get 2 Y's and an N you've got A or D in truth mode, so ask was the first answer a lie. If they answer Y then B is any of their N answers, if they answer Y you've got D in truth.[/size]


Tennis Balls doesn't even take math
[size=7]3<pi---so wrap is longer than up the side---I'd go for up the side, though, it's more visible[/size]

6 digit number
[size=7]A9543B= 795432
A=7[/size]


Average plus 10
[size=7]Average=(5*16+10)/6=15[/size]

4 digit number
[size=7]3AA1=3771
A=7[/size]


Marbles
[size=7]Has to be 60 Bob?-the universal composite. The Babylonians were right
2^2*3*5=60
2=2
3=3
2*2=4
2*3=6
5=5
also works for 10, 12, 15, & 30[/size]


Rap c∫;?/
0 Replies
 
whimsical
 
  1  
Reply Tue 2 Aug, 2005 03:15 am
I would think you'd see the 75 meter high lighthouse on a ~2 hectare island, so no questions are needed.
0 Replies
 
Tryagain
 
  1  
Reply Tue 2 Aug, 2005 05:55 am
Mark:

TENNIS BALLS
Since pi > 3, ... Cool

A9543B
7 Cool

SIX NUMBERS
15 Cool

3AA1
7 Cool

MARBLES
60 Cool

Ask "Do you always tell the truth?" until you get a "no" response. Then ask this person which road leads to the lighthouse.
The only person who will answer "no" is person three. Since person three just told the truth, he will answer a follow-up question truthfully.

Pick one (call him A). Ask these three questions:
Does B always tell the truth?
Does C always tell the truth?
Does D always tell the truth?

Person one will answer with "no, no, no."
Persons two and four will answer (perhaps not in this order) with "no, yes, yes" where the "no" applies to person one.
Person three will answer (perhaps not in this order) with "yes, no, no" where the "yes" applies to person one.

If you get "no, no, no," then ask that same person which road to take.
If you get "no, yes, yes," then ask the person that the "no" applied to which road to take.
If you get "yes, no, no," then ask that same person or the person that the "yes" applied to which road to take.


Rap:

Rocky Island Guides

I opine there are no more than four questions to get to the teller's of truth in all cases Cool

I'll label the guides A,B,C&D.
A Lies
B is Truthful
C Starts with the Truth, then lies
D Starts with a Lie, then becomes Truthful

Start with three questions about the certifiable honestly of the others.

If A (BCD-NYY) (BDC)-NYY) (CBD-YNY) (CDB-YYN) (DBC-YNY) (DCB-YYN)
If B (ACD-NNN) (ADC_NNN) (CAD-NNN) (CDA_NNN) (DAC-NNN) (DCA-NNN)
If C (ABD-NNY) (ADB-NYN) (BAD-YYY) (DBA-NNY) (BAD-YYY) (BDA-YYY)
If D (ABC-YYN) (ACB-YNN) (BAC-NNN) (BCA-NNN) (CBA-YYN) (CAB-YNY)

If you get three N ask them. You've either got B or D in truth
If you get three Y you've got C as liar, so ask ?'Who never lies?', and he'll get you to B.
If you get two N's and a Y you've got C as liar, ask the same question to get B
If you get 2 Y's and an N you've got A or D in truth mode, so ask was the first answer a lie. If they answer Y then B is any of their N answers, if they answer Y you've got D in truth.

Tennis Balls doesn't even take math
3<pi---s Cool o wrap is longer than up the side---I'd go for up the side, though, it's more visible

6 digit number
A9543B= 795432
A=7 Cool

Average plus 10
Average=(5*16+10)/6=15 Cool

4 digit number
3AA1=3771
A=7 Cool

Marbles
Has to be 60 Bob?-the universal composite. The Babylonians were right
2^2*3*5=60 Cool
2=2
3=3
2*2=4
2*3=6
5=5
also works for 10, 12, 15, & 30


Dear Mark and Rap, thank you for your answers to the Lighthouse problem. My answer did not fully address the problem, Embarrassed so I had a fallback, eloquently expressed by;

Whim:
"I would think you'd see the 75 meter high lighthouse on a ~2 hectare (a flat) island, so no questions are needed." Cool

Rap wrote, "Tennis Balls doesn't even take math" Shocked

Well, excuse me! Whilst I accept some questions may not challenge a ?'white water wizard', I thought there might be a few people out there down at my level. However, from the lack of any new response, it would appear not. Crying or Very sad

Therefore, to show I bear no grudge, you want mathÂ… you got math. Twisted Evil


The great Pyramids at Giza in Egypt were built nearly 5,000 years ago as tombs for the Pharaohs. They are very big. The largest is Kheops, which is 146 meters high and has a square base that is 230 meters on each side. Khephren is 143 meters high with a square base 215 meters on a side. The smallest is Mykerinos, which is 66 meters high and has a base 108 meters on each side.

Legend has it that when Napoleon and Rap visited them he calculated that there was enough stone in them to build a wall around France, 3 meters high and 30 centimeters thick. Napoleon was not so sure. Two local Pharaohs, Mark and Whim thought; around Paris and along the land boarder only. I don't think any would work.

Who was correct Question


For those who can not stand math:

1. Why is a crossword puzzle like a quarrel Question

2. Why is a bad cold like a great humiliation Question

3. Why is a schoolboy being paddled like your eye Question

4. What time is it when the clock strikes thirteen Question

5. What is black and white and red all over Question
0 Replies
 
markr
 
  1  
Reply Tue 2 Aug, 2005 09:24 am
[size=7]PYRAMIDS
The pyramids will provide nearly 5600km of wall.
Assuming France is square (it's not, but it's not too far off from being squarish), its area would have a perimeter of about 3000km. I'd say the wall could completely surround France.
[/size]
0 Replies
 
Tryagain
 
  1  
Reply Tue 2 Aug, 2005 03:51 pm
One day on a stopover in New York as the temperature hit the high 80's, I bought an ice-cold container of water. I casually glanced at the label which read; ?'NET WT. 1 GAL (128 FL OZ) 3.78 L'

You may well have a similar container of this popular brand. My question, should you be brave enough to accept is:

What's wrong with the label Question
0 Replies
 
raprap
 
  1  
Reply Tue 2 Aug, 2005 08:19 pm
Pyramids
[size=7]Ans---Just about
Volume of pyramid
V=1/3bh where b is base area and h is height

Cheops=1/3*146m (230m)^2=2,574,000m^3
Chaperon =1/3*143m (215m)^2=2,203,000m^3
Michelins =1/3*66m (108m)^2=256,000m^3
Vall=(2,574+2,203+256)*1000=5034,000m^3

Wall 3m tall and 0,3M wide TAKES 0.9M^3/Mlength

Wall length is Vall/0.9=5,593,000m=5,593km

France Factoids
Land boundary (Belgium, Germany, Switzerland, Spain, and one of those teeny countries in the Pyrenees) =2893km
Coastline=3427 km
Total 6319km

Can they build a wall around France---Shy about 726km (that's about 430 miles to us ?'Mericans).[/size]


1. Why is a crossword puzzle like a quarrel--it's full of cross words

4. What time is it when the clock strikes thirteen--time to call the repairman

5. What is black and white and re(a)d all over--newspaper

Rap c∫;?/
0 Replies
 
raprap
 
  1  
Reply Tue 2 Aug, 2005 08:46 pm
Label--Actually nothing. Most liquids are sold in containers based upon liquid weight measure conversions. Say a liter volume weighs 1 kg when filled with water, and a US Gallon is (about) 128 fluid oz (of water).

However this conversion does lead to an interesting difference---fer instance

conversion from gal to liter (by weight) is
1 gal=(128/16)/2.2=3.6 kg=3.6L
and by Vol, it is
1 gal=231*(2.54)^3/1000=3.78L
remembering 1 gal=231 cubic inches

Rap
0 Replies
 
markr
 
  1  
Reply Wed 3 Aug, 2005 12:22 am
A gallon is a unit of capacity, not weight. The density of the contents will determine the weight.

The liquids in my pantry are labeled by capacity (fluid ounces), not weight.
0 Replies
 
markr
 
  1  
Reply Wed 3 Aug, 2005 12:32 am
PYRAMIDS
Wow! My back of the napkin conversion of area to perimeter was off by a factor of 2.
0 Replies
 
Tryagain
 
  1  
Reply Wed 3 Aug, 2005 03:03 pm
Mark:

PYRAMIDS
The pyramids will provide nearly 5600km of wall. Cool

Rap:

Pyramids
Ans---Just about Cool
Volume of pyramid
V=1/3bh where b is base area and h is height

Cheops=1/3*146m (230m)^2=2,574,000m^3
Chaperon =1/3*143m (215m)^2=2,203,000m^3
Michelins =1/3*66m (108m)^2=256,000m^3
Vall=(2,574+2,203+256)*1000=5034,000m^3

Wall 3m tall and 0,3M wide TAKES 0.9M^3/Mlength

Wall length is Vall/0.9=5,593,000m=5,593km Cool

France Factoids
Land boundary (Belgium, Germany, Switzerland, Spain, and one of those teeny countries in the Pyrenees) =2893km
Coastline=3427 km
Total 6319km

Can they build a wall around France---Shy about 726km (that's about 430 miles to us ?'Mericans).


Mark, "Wow! My back of the napkin conversion of area to perimeter was off by a factor of 2."


FANTASTIC calculations guys. Cool Cool Mark, if you abandon the ?'napkin' and return to the abacus you will avoid such errors. Laughing


To start with, we have to figure out how much stone is in the Pyramids. Although there is a small amount of open space inside each Pyramid for the Pharaoh and his stuff, this is tiny compared to the overall volume. For this puzzle we can assume the Pyramids to be solid stone.

The formula for the volume of a pyramid is
V = 1/3 * H * Ab
Where V is volume, H is the height of the pyramid and Ab is the area of the base. Starting with Kheops, the square base is 230 meters on a side, so the area is 52,900 square meters. The height is 146 meters. So
V = 1/3 * 146 * 52,900 = 2,574,467 cubic meters

Following the same procedure we find that the volume of Khephren is 2,203,392 cubic meters and the volume of Mykerinos is 256,608 cubic meters. The total volume of the three Pyramids is 5,034,467 cubic meters.
Now let's look at Napoleon's proposed wall. How much stone would be needed to build a section 1 kilometer long? The volume of such a rectangle is Height * Length * Width. The Length is 1 kilometer, or 1,000 meters. The Height is 3 meters and the width is 30 cm, or 0.3 meters. So
V = 1,000 * 3 * 0.3 = 900 cubic meters

Every 900 cubic meters of stone makes a wall 1 kilometer long. Dividing the total volume of the stone in the Pyramids by the amount of stone in a 1 km section gives us the length, in kilometers, of the wall that could be built:

Length of Napoleon's proposed wall around France = 5,034,467 / 900 = 5,594 kilometers. Is that enough to go all the way around the country?

If you draw a square on a map of France 1,000 km on a side. The perimeter is 4,000 km. So we've built a wall around France with 1,594 km of stone wall to spare.

But this is probably not what Napoleon had in mind. What if the wall followed the coastline and the boundaries with neighboring countries? Would there be enough stone for such a wall? We can't answer that because we can't know how long the boundary is. This may seem surprising, but the length of the boundary depends on how big a ruler you use to measure it. The smaller the ruler, the longer the path. Shocked


Water:

Rap Cool

Label--Actually nothing. Most liquids are sold in containers based upon liquid weight measure conversions. Say a liter volume weighs 1 kg when filled with water, and a US Gallon is (about) 128 fluid oz (of water).


Mark: Cool

A gallon is a unit of capacity, not weight. The density of the contents will determine the weight.

The liquids in my pantry are labeled by capacity (fluid ounces), not weight.


?'The label says "NET WT. 1 GAL," which is an abbreviation for "Net Weight 1 Gallon." The label is saying that the weight of the water is 1 gallon.

The problem is that the gallon is a unit of volume, not weight.

The gallon is a measure used in the United States. Its metric equivalent is 3.78 liters, which is also on the label.

But the mistake is not completely off the mark. Knowing that you have 1 gallon of water also tells you what it weighs. As the label says, a gallon is equal to 128 fluid ounces. A fluid ounce is a measure of volume, like the gallon. But there is a unit of weight called an "ounce" that is the weight of one fluid ounce of water.

Therefore, the water weighs 128 ounces, or 8 pounds. (There are 16 ounces in a pound).'



1. Why is a crossword puzzle like a quarrel?
.....Because one word leads to another.

2. Why is a bad cold like a great humiliation?
.....Because it brings the proudest man to his sneeze.

3. Why is a schoolboy being paddled like your eye?
.....Because he is a pupil under a lash.

4. What time is it when the clock strikes thirteen?
.....Time to get a new clock.

5. What is black and white and red all over?
.....An embarrassed zebra (not a newspaper which is "READ")



A book has 500 pages numbered 1, 2, 3, and so on. How many times does the digit 1 appear in the page numbers Question

In three bowling games, Alice scores 139, 143, and 144. What score Will Alice need in a fourth game in order to have an average score of 145 for all four games Question

P and Q represent numbers, and P * Q means (P+Q)/2 . What is the value of 3 * (6 * 8) Question

If 1/3 = 1/A + 1/B where A and B are different whole numbers, find the value of A and the value of B Question

Serious logic riddles:

Two men were drinking in a bar. Two women walked in. The first man said, "I have to go, my wife and daughter are here." The second man turned around and said, "I have to go too, my wife and daughter just arrived as well." How is this possible Question

Clues: No-one else has walked in apart from these two women. The men are not married to the same woman.


A windowless room has 3 light bulbs. Three switches are outside the room, and each switch operates one of the bulbs inside. If you only enter the room once, how can you determine which bulb is connected to which switch Question


Why do Chinese men eat more rice than Japanese men Question
(Yes, this is serious.)
0 Replies
 
markr
 
  1  
Reply Wed 3 Aug, 2005 05:47 pm
[size=7]BOOK
100+5*10+5*10 = 200

BOWLING
154

P AND Q
5

1/A + 1/B
4 and 12

WIVES AND DAUGHTERS
The younger one could be pregnant with a baby girl.

LIGHT BULBS
Turn two of the switches on for 30 sec.
Turn one of them off.
The hot bulb that is off goes with the switch that was on then off. The others are obvious.

RICE
There are a lot more Chinese men than Japanese men.
[/size]
0 Replies
 
 

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