Ok... after this I am taking a few hours off.... Maths is hard work...

Correct Bill,
The answer is 0 and at the 32nd Decimal Place.... 1/2 "Well Earned" Point to Scary Capitalist...

Standings:
1. WinterKnight - 3 Points
2. Mr. Kevvy - 2 Points
3. William Rothamel - 2 Points
4. John McLeod VII - 1 Point
5. Scary Capitalist - 1/2 Point
6. TBD....


10. Partial differential equations required.
Water flows into a tank at a rate of 1 gallon per second. Water leaves the tank at a rate of 1 gallon per second for each 100 gallons in the tank.
The tank is initially empty. How long will it take for the tank to fill with 50 gallons of water?

11. Integral calculus and trigonometry required.
What is the mean distance between two random points in a unit square?

12. Simple Maths Questions
A traveller comes to India, he introduces the number 0 to their King, the king there are so amazed by this new number that
he promises anything in return. All the traveller asks for is a grain of rice that doubles for every chess square.. e.g. Square 1 = 1 rice grain, Square 2 = 2 Rice Grains, Square 3 = 4 Rice Grains... so on....

12a. Which Chess Square will contain 4096 grains of rice.?
12b. How many grains are on the 18th square?
12c. Which Chess Square will contain 32768 grains of rice?
12d. How much rice does the first half of the Chessboard Contain?
12e. How much rice is there the 64th Square alone?
12f. How much rice is there on the whole chessboard?

(To score a Point, you must answer all 6 correctly, no half points allowed)

(Also: No giving away points from now on... lol)


I now stake a claim as the largest Maths thread in the Cafe!!!!

Have a try & Best Regards,
Luke.

---

- Luke.

Sweeeet. I weaseled my way into 1/2 point on my good looks.

---

Founder of BOINC team Objectivists. Oh the humanity! Rational people crunching data!
I did NOT authorize this belly writing!

b=the mean distance would have to be the distance of corner to corner. In other words 1/2 of the length of C.

simple pythagoreanism right
?

---

Founder of BOINC team Objectivists. Oh the humanity! Rational people crunching data!
I did NOT authorize this belly writing!

You see that DADDIO is expert on the digits of Pi since he has been crunching for the BOINC math conjectures project.

Ok... after this I am taking a few hours off.... Maths is hard work...

Correct Bill,
The answer is 0 and at the 32nd Decimal Place.... 1/2 "Well Earned" Point to Scary Capitalist...

Standings:
1. WinterKnight - 3 Points
2. Mr. Kevvy - 2 Points
3. William Rothamel - 2 Points
4. John McLeod VII - 1 Point
5. Scary Capitalist - 1/2 Point
6. TBD....


10. Partial differential equations required.
Water flows into a tank at a rate of 1 gallon per second. Water leaves the tank at a rate of 1 gallon per second for each 100 gallons in the tank.
The tank is initially empty. How long will it take for the tank to fill with 50 gallons of water?

11. Integral calculus and trigonometry required.
What is the mean distance between two random points in a unit square?

12. Simple Maths Questions
A traveller comes to India, he introduces the number 0 to their King, the king there are so amazed by this new number that
he promises anything in return. All the traveller asks for is a grain of rice that doubles for every chess square.. e.g. Square 1 = 1 rice grain, Square 2 = 2 Rice Grains, Square 3 = 4 Rice Grains... so on....

12a. Which Chess Square will contain 4096 grains of rice.?
12b. How many grains are on the 18th square?
12c. Which Chess Square will contain 32768 grains of rice?
12d. How much rice does the first half of the Chessboard Contain?
12e. How much rice is there the 64th Square alone?
12f. How much rice is there on the whole chessboard?

(To score a Point, you must answer all 6 correctly, no half points allowed)

(Also: No giving away points from now on... lol)


I now stake a claim as the largest Maths thread in the Cafe!!!!

Have a try & Best Regards,
Luke.

Hey Hey Hey --Congrats on starting a classic thread. Maybe should make your problems a little easier I consider myself to be above average (only old now) yet usually stumble around with your problems.

Fine contribution,

Regards,

Bill

Ok... after this I am taking a few hours off.... Maths is hard work...

Correct Bill,
The answer is 0 and at the 32nd Decimal Place.... 1/2 "Well Earned" Point to Scary Capitalist...

Standings:
1. WinterKnight - 3 Points
2. Mr. Kevvy - 2 Points
3. William Rothamel - 2 Points
4. John McLeod VII - 1 Point
5. Scary Capitalist - 1/2 Point
6. TBD....


10. Partial differential equations required.
Water flows into a tank at a rate of 1 gallon per second. Water leaves the tank at a rate of 1 gallon per second for each 100 gallons in the tank.
The tank is initially empty. How long will it take for the tank to fill with 50 gallons of water?

11. Integral calculus and trigonometry required.
What is the mean distance between two random points in a unit square?

12. Simple Maths Questions
A traveller comes to India, he introduces the number 0 to their King, the king there are so amazed by this new number that
he promises anything in return. All the traveller asks for is a grain of rice that doubles for every chess square.. e.g. Square 1 = 1 rice grain, Square 2 = 2 Rice Grains, Square 3 = 4 Rice Grains... so on....

12a. Which Chess Square will contain 4096 grains of rice.?
12b. How many grains are on the 18th square?
12c. Which Chess Square will contain 32768 grains of rice?
12d. How much rice does the first half of the Chessboard Contain?
12e. How much rice is there the 64th Square alone?
12f. How much rice is there on the whole chessboard?

(To score a Point, you must answer all 6 correctly, no half points allowed)

(Also: No giving away points from now on... lol)


I now stake a claim as the largest Maths thread in the Cafe!!!!

Have a try & Best Regards,
Luke.

Hey Hey Hey --Congrats on starting a classic thread. Maybe should make your problems a little easier I consider myself to be above average (only old now) yet usually stumble around with your problems.

Fine contribution,

Regards,

Bill

If you yell loud enough you might get awarded 1/2 point out of pity...

---

Founder of BOINC team Objectivists. Oh the humanity! Rational people crunching data!
I did NOT authorize this belly writing!

12a. Which Chess Square will contain 4096 grains of rice.?
12b. How many grains are on the 18th square?
12c. Which Chess Square will contain 32768 grains of rice?
12d. How much rice does the first half of the Chessboard Contain?
12e. How much rice is there the 64th Square alone?
12f. How much rice is there on the whole chessboard?

12a. Which Chess Square will contain 4096 grains of rice.?
The 13th square.

12b. How many grains are on the 18th square?
131,072

12c. Which Chess Square will contain 32768 grains of rice?
The 16th

12d. How much rice does the first half of the Chessboard Contain?
That would be the first 32 squares, up to 2^31, which sums to 2^32-1 grains (because sum from 0 to n of 2^n is 2^(n+1)-1) or
4,294,967,295 grains

12e. How much rice is there the 64th Square alone?
9,223,372,036,854,775,808 grains

12f. How much rice is there on the whole chessboard?
As above, 2^64-1 grains or
18,446,744,073,709,551,615 grains

---

Correct Answers Mr. Kevvy....
Official Answers to 12"x" questions are in Mr. Kevvy's post above.

Standings So Far:
1. WinterKnight - 3 Points
2. Mr. Kevvy - 3 Points
3. William Rothamel - 2 Points
4. John McLeod VII - 1 Point
5. Scary Capitalist - 1/2 Point
6. TBD....

@William Rothamel: lol, love the Comic. Also, thanks for your tip, I will make latter questions more easier, to pull in more mathematicians
@Scary Capitalist: You got your answer to 11 wrong.... sorry mate!
@Everyone: Have a go!!!!

Remaining Questions:
10. Partial differential equations required.
Water flows into a tank at a rate of 1 gallon per second. Water leaves the tank at a rate of 1 gallon per second for each 100 gallons in the tank.
The tank is initially empty. How long will it take for the tank to fill with 50 gallons of water?

11. Integral calculus and trigonometry required.
What is the mean distance between two random points in a unit square?

---

- Luke.

Never mind... I just duplicated ScaryCapitalist's answer, so I retract mine. Guess I have to do it the hard way. :^p

---

12a. Which Chess Square will contain 4096 grains of rice.?
12b. How many grains are on the 18th square?
12c. Which Chess Square will contain 32768 grains of rice?
12d. How much rice does the first half of the Chessboard Contain?
12e. How much rice is there the 64th Square alone?
12f. How much rice is there on the whole chessboard?

12a. Which Chess Square will contain 4096 grains of rice.?
The 13th square.

12b. How many grains are on the 18th square?
131,072

12c. Which Chess Square will contain 32768 grains of rice?
The 16th

12d. How much rice does the first half of the Chessboard Contain?
That would be the first 32 squares, up to 2^31, which sums to 2^32-1 grains (because sum from 0 to n of 2^n is 2^(n+1)-1) or
4,294,967,295 grains

12e. How much rice is there the 64th Square alone?
9,223,372,036,854,775,808 grains

12f. How much rice is there on the whole chessboard?
As above, 2^64-1 grains or
18,446,744,073,709,551,615 grains

Nuts. An easy one and I wasn't around to answer it in time.

---

BOINC WIKI

LUKE, is it okay that I post an occasional joke in your thread without it being deleted as OFF TOPIC by the moderators?

You are the thread founder. Perhaps the communications i keep trying to post for you/us since we lived in the same country could now recommence?


Maybe if you posted 'yes' they will stop deleting my messages to you and to this board in general.

They've tried the same censorship stunt over in Ice's chess thread.

---

Founder of BOINC team Objectivists. Oh the humanity! Rational people crunching data!
I did NOT authorize this belly writing!

LUKE, is it okay that I post an occasional joke in your thread without it being deleted as OFF TOPIC by the moderators?

You are the thread founder. Perhaps the communications i keep trying to post for you/us since we lived in the same country could now recommence?


Maybe if you posted 'yes' they will stop deleting my messages to you and to this board in general.

They've tried the same censorship stunt over in Ice's chess thread.

Jokes are fine, from now on they will be considered "ON-TOPIC" in this thread, I will notify people if it starts to get too "off-topic" though....
And everyone still has to remember the main goal here is to defeat my all powerful, amazing wrath of math questions.....

@John McLeod....
Once Q10 & Q11 are complete I will post some easier ones.... new rules will apply to the easier ones though.... I will announce them here later....

Best Regards & Keep on solving,
Luke.

---

- Luke.

11. Integral calculus and trigonometry required.
What is the mean distance between two random points in a unit square?

.5214

11. Integral calculus and trigonometry required.
What is the mean distance between two random points in a unit square?

.5214

Well Done Bill!!!.....
Official Answer Q11: 0.521405

Standings:
1. WinterKnight - 3 Points
2. Mr. Kevvy - 3 Points
3. William Rothamel - 3 Points
4. John McLeod VII - 1 Point
5. Scary Capitalist - 1/2 Point
6. TBD....

A Triple Tie for 1st Place!!!!


Question 10 Remains.......

10. Partial differential equations required.
Water flows into a tank at a rate of 1 gallon per second. Water leaves the tank at a rate of 1 gallon per second for each 100 gallons in the tank.
The tank is initially empty. How long will it take for the tank to fill with 50 gallons of water?

Luke.

---

- Luke.

10. Partial differential equations required.
Water flows into a tank at a rate of 1 gallon per second. Water leaves the tank at a rate of 1 gallon per second for each 100 gallons in the tank.
The tank is initially empty. How long will it take for the tank to fill with 50 gallons of water?

Phooey on partial differential equations! :^p Tried this several times with calculus and gave up getting as far as integrating both sides. Too rusty I am. I settled for an imperfect numerical analysis by writing a tiny Python script:

def fill(n):
	V, t = 0.000000, 0.000000
	while V < 50:
		V, t = V-((V*n)/100)+n, t+n
	print V, t

This will provide a closer and closer approximation with smaller values of n.

>>> fill(1)
50.0162970101 69.0

69 seconds there...

>>> fill(.001)
50.0003142596 69.315

69.315 seconds there, now have perhaps four digits correct.

>>> fill(0.000001)
50.0000000894 69.314717917

This took about 15 seconds even on a quad, sucking cycles from SAH. Notice how close the V value now is to 50. I found what that t value is. ln(2) is 0.69314718055994530941723212145818 to as many digits as Windows calculator will deliver. t is close enough to 100ln(2) (which would make perfect sense as the natural log turns up in the integral) that I can call that the answer.

Yes, these problems are not easy. :^)

---

Again answer is correct, Mr. Kevvy!
Official Question 10 Answer: 69.315 Seconds....

Standings so far:
1. Mr. Kevvy - 4 Points
2. WinterKnight - 3 Points
3. William Rothamel - 3 Points
4. John McLeod VII - 1 Point
5. Scary Capitalist - 1/2 Point
6. TBD....

Thanks everyone for all your feedback on these questions....
I have now laid out basic rules for this thread - MUST READ!!! -....

A. No Flaming....
B. Jokes and math are considered "ON-TOPIC", anything else is most likely "OFF-TOPIC".
C. Follow the posting rules
D. In a group of 3 maths questions posted... 2 will be EASY and 1 will be HARD,
Easy earns you a 1/2 Point.... Hard earns you 1 Point....
E. You may only answer 2 Per group.... leave the other one for someone else to even the standings out...
F. Contact me if you have any ideas/questions....

Here are the next bunch of questions:

13. EASY - Esther drove to work in the morning at an average speed of 45 miles per hour. She returned home in the evening along the same route and averaged 30 miles per hour. If Esther spent a total of one hour commuting to and from work, how many miles did Esther drive to work in the morning?

14. EASY - You have two blocks of clay in cube form and the edges are 10 cm. How many spheres with a radius of 5 cm can you make with that amount of clay?

15. HARD -The police commissioner hired a mathematician to help at a crime scene. At the scene were between 100 and 200 glasses of wine. Exactly one glass was poisoned. The police lab could test any sampling for poison. A group of glasses could be tested simultaneously by mixing a sample from each glass. The police commissioner desires only to minimize the maximum possible tests required to determine which exact glass was poisoned. The mathematician started by asking a detective to select a single glass at random for testing. "Wouldn't that waste a test?", the detective asked. "No, besides I'm in a gambling mood.", the mathematician replied. How many glasses were there?

Have a go.... are there any other mathematicians out there?

Luke.

---

- Luke.

#14 answer is 19 with some clay left over.######## Oops forgot to divide by the last 5 Kevvy beats me again.

regards,

Bill

#13 is 18 miles

15. HARD -The police commissioner hired a mathematician to help at a crime scene. At the scene were between 100 and 200 glasses of wine. Exactly one glass was poisoned. The police lab could test any sampling for poison. A group of glasses could be tested simultaneously by mixing a sample from each glass. The police commissioner desires only to minimize the maximum possible tests required to determine which exact glass was poisoned. The mathematician started by asking a detective to select a single glass at random for testing. "Wouldn't that waste a test?", the detective asked. "No, besides I'm in a gambling mood.", the mathematician replied. How many glasses were there?

I go with 129 glasses. 128 is a power of 2, and he wants the group to be an even power of two for elimination-by-halves testing, so the 129th is the odd one out.

14. EASY - You have two blocks of clay in cube form and the edges are 10 cm. How many spheres with a radius of 5 cm can you make with that amount of clay?

You have 2x10^3 or 2,000cc of clay. Volume of sphere is 4/3 Pi r^3 so for a 5cm radius sphere is ~523cc. So you could make only 3 spheres and have about 430cc of clay left over.

---

15. HARD -The police commissioner hired a mathematician to help at a crime scene. At the scene were between 100 and 200 glasses of wine. Exactly one glass was poisoned. The police lab could test any sampling for poison. A group of glasses could be tested simultaneously by mixing a sample from each glass. The police commissioner desires only to minimize the maximum possible tests required to determine which exact glass was poisoned. The mathematician started by asking a detective to select a single glass at random for testing. "Wouldn't that waste a test?", the detective asked. "No, besides I'm in a gambling mood.", the mathematician replied. How many glasses were there?

I go with 129 glasses. 128 is a power of 2, and he wants the group to be an even power of two for elimination-by-halves testing, so the 129th is the odd one out.

14. EASY - You have two blocks of clay in cube form and the edges are 10 cm. How many spheres with a radius of 5 cm can you make with that amount of clay?

You have 2x10^3 or 2,000cc of clay. Volume of sphere is 4/3 Pi r^3 so for a 5cm radius sphere is ~523cc. So you could make only 3 spheres and have about 430cc of clay left over.

The actual answer is 3.819721 so 430/523 is the .819721 as Kevvy points out