Damn I love Mathematics!

[GuyFromSingapore]

Combinatorial Problem, Determining Existence:

Four married couples play mixed double tennis on two courts each Sunday night. They play for 2 hours, but switch partners and opponents after each half hour period. Does a schedule exist so that each man plays with and against each woman exactly once, and plays against each other man at least and at most twice?

Answer: think of it as 4 coins(heads and tails, 4 married couples. Sides/couples.) constantly flipping and facing each other.

Now change each heads and tails of the different coins and combine them in different combinations and flip the coins again each time.

 

[jd922]

high iq asian i guess

 

[lcberg04]

I hate you Asian math wizards make me feel stupid every damn time

 

[GuyFromSingapore]

high iq asian i guess

Curry.

Only 135(as per Mensa Norway).

 

[lnceIs]

dnr

 

[GuyFromSingapore]

I hate you Asian math wizards make me feel stupid every damn time

I'm Curry, Bhai.

 

[jd922]

Curry.

Only 135(as per Mensa Norway).

good shit brah mirin

 

[GuyFromSingapore]

Hint: the question is complicated because they keep switching partners and opponents.

 

[GuyFromSingapore]

Mathematical Induction

 

[Jesus_ist_König]

I hate you Asian math wizards make me feel stupid every damn time

I love maths
"Never trust a true" - Nicola Tesla

 

[GuyFromSingapore]

 

[GuyFromSingapore]

 

[topology]

Combinatorial Problem, Determining Existence:

Four married couples play mixed double tennis on two courts each Sunday night. They play for 2 hours, but switch partners and opponents after each half hour period. Does a schedule exist so that each man plays with and against each woman exactly once, and plays against each other man at least and at most twice?

Answer: think of it as 4 coins(heads and tails, 4 married couples. Sides/couples.) constantly flipping and facing each other.

Now change each heads and tails of the different coins and combine them in different combinations and flip the coins again each time.

M = {m0,m1,m2,m3}
W = {w0,w1,w2,w3}
F2_2 = {(0,0),(0,1),(1,0),(1,1)}

Each man and woman gets a label x ∈ F2_2

Round t : Mx partners Wx+t

For t ∈ F2_2

For fixed x, as t turns over all 4 elements: x + t = all elements of F2_2

So: each man partners each woman exactly once (1)

In each round t, we must split the 4 pairs into 2 matches)

D ∈ F2_2, d != 0

Partition: {x, x+d} form a match

So each match is: (Mx, Wx+t) vs (Mx+d, Wx+d+t)

There are 3 choices of d != 0: (1,0), (0,1), (1,1)

For women, fix a man Mx.

In round t, he plays against: Wx+d+t

As t varies over all 4 values: x + d + t runs over all ∈ F2_2

So: Each man plays against each woman exactly once (2)

Now, for men, fix two distinct men Mx, My.

They play against each other if: y = x + d (each round uses exactly one value of d, so over 4 rounds you choose d1, d2, d3, d4 ∈ F2_2 \ {0}. Each round determines which pairs of men face each other)

So:

For each round, a man faces exactly one specific other man

Over 4 rounds, we choose d's so that:

Each difference y - x != 0 appears:

At least once and at most twice

There are 3 nonzero differences. We have 4 rounds. So we assign:

Each difference once (3 rounds)

One difference repeated (4th round)

Thus: each pair of men meets 1 or 2 times (3)

 

[topology]

M = {m0,m1,m2,m3}
W = {w0,w1,w2,w3}
F2_2 = {(0,0),(0,1),(1,0),(1,1)}

Each man and woman gets a label x ∈ F2_2

Round t : Mx partners Wx+t

For t ∈ F2_2

For fixed x, as t turns over all 4 elements: x + t = all elements of F2_2

So: each man partners each woman exactly once (1)

In each round t, we must split the 4 pairs into 2 matches)

D ∈ F2_2, d != 0

Partition: {x, x+d} form a match

So each match is: (Mx, Wx+t) vs (Mx+d, Wx+d+t)

There are 3 choices of d != 0: (1,0), (0,1), (1,1)

For women, fix a man Mx.

In round t, he plays against: Wx+d+t

As t varies over all 4 values: x + d + t runs over all ∈ F2_2

So: Each man plays against each woman exactly once (2)

Now, for men, fix two distinct men Mx, My.

They play against each other if: y = x + d (each round uses exactly one value of d, so over 4 rounds you choose d1, d2, d3, d4 ∈ F2_2 \ {0}. Each round determines which pairs of men face each other)

So:

For each round, a man faces exactly one specific other man

Over 4 rounds, we choose d's so that:

Each difference y - x != 0 appears:

At least once and at most twice

There are 3 nonzero differences. We have 4 rounds. So we assign:

Each difference once (3 rounds)

One difference repeated (4th round)

Thus: each pair of men meets 1 or 2 times (3)

The formatting is very bad as I never spent the time to properly do proofs.

The reason I didn't get top 5 for all contests I participated in is due to this + being mediocre at geometry.

 

[GuyFromSingapore]

M = {m0,m1,m2,m3}
W = {w0,w1,w2,w3}
F2_2 = {(0,0),(0,1),(1,0),(1,1)}

Each man and woman gets a label x ∈ F2_2

Round t : Mx partners Wx+t

For t ∈ F2_2

For fixed x, as t turns over all 4 elements: x + t = all elements of F2_2

So: each man partners each woman exactly once (1)

In each round t, we must split the 4 pairs into 2 matches)

D ∈ F2_2, d != 0

Partition: {x, x+d} form a match

So each match is: (Mx, Wx+t) vs (Mx+d, Wx+d+t)

There are 3 choices of d != 0: (1,0), (0,1), (1,1)

For women, fix a man Mx.

In round t, he plays against: Wx+d+t

As t varies over all 4 values: x + d + t runs over all ∈ F2_2

So: Each man plays against each woman exactly once (2)

Now, for men, fix two distinct men Mx, My.

They play against each other if: y = x + d (each round uses exactly one value of d, so over 4 rounds you choose d1, d2, d3, d4 ∈ F2_2 \ {0}. Each round determines which pairs of men face each other)

So:

For each round, a man faces exactly one specific other man

Over 4 rounds, we choose d's so that:

Each difference y - x != 0 appears:

At least once and at most twice

There are 3 nonzero differences. We have 4 rounds. So we assign:

Each difference once (3 rounds)

One difference repeated (4th round)

Thus: each pair of men meets 1 or 2 times (3)

I'll work on this and try to figure out if you've solved this.

Meanwhile recommend me some good Maths books to build solid foundation as precursor to University Mathematics. Especially books the explain symbols.

 

[topology]

Meanwhile recommend me some good Maths books to build solid foundation as precursor to University Mathematics. Especially books the explain symbols.

Symbols wouldn't take more than like a day to learn online.

I don't use math books either. I find something I want to learn, find a simple problem within it, and ask AI to help me with the steps. It's superior to learning all the foundations first as you won't be overloaded & you'll enjoy the process.

 

[GuyFromSingapore]

Symbols wouldn't take more than like a day to learn online.

I don't use math books either. I find something I want to learn, find a simple problem within it, and ask AI to help me with the steps. It's superior to learning all the foundations first as you won't be overloaded & you'll enjoy the process.

Come on man. Surely you've read a couple of books.

 

[Deleted member 351479]

Mirin
​

 

[topology]

Come on man. Surely you've read a couple of books.

I bought books but never got around to reading them. I had to obviously buy books for university but I just used online resources to get by. I've yet to seriously read books unless it's very specific to what I'm learning.

 

[GuyFromSingapore]

I bought books but never got around to reading them. I had to obviously buy books for university but I just used online resources to get by. I've yet to seriously read books unless it's very specific to what I'm learning.

Ok give me the list of books you're using for University. Are you a Pure or Applied Maths major?

 

[topology]

Ok give me the list of books you're using for University. Are you a Pure or Applied Maths major?

Computer science. I've been studying math in my free time for years now too.

I can obviously give you some books but they're very unintuitive. You won't be able to learn from them. I can give examples from a elementary number theory book I have beside me if you wish & tell me if you still want some after that. It takes 10x longer to manually learn with books rather than just using AI.

 

[GuyFromSingapore]

Computer science. I've been studying math in my free time for years now too.

I can obviously give you some books but they're very unintuitive. You won't be able to learn from them. I can give examples from a elementary number theory book I have beside me if you wish & tell me if you still want some after that. It takes 10x longer to manually learn with books rather than just using AI.

Give me examples.

Also I need explanations of symbols. I don't have a laptop, I'm only using a smartphone so I can't type symbols. Need to download an App.

 

[topology]

Give me examples.

This is how it taught induction:

I personally wasn't able to learn with this.. YouTube taught me it in about 15 minutes vs this garbage. It's almost made in a way where they can say the substance is there but you cannot learn off it. It's made difficult as they don't care enough to simplify it. You may find it easy as you know the subject now but no one I showed it to was able to figure it out. Keep in mind induction is an easy topic to learn.

Random page I found with more complex problems:

 

[GuyFromSingapore]

This is how it taught induction:
View attachment 4907022View attachment 4907033View attachment 4907032View attachment 4907029

I personally wasn't able to learn with this.. YouTube taught me it in about 15 minutes vs this garbage. It's almost made in a way where they can say the substance is there but you cannot learn off it. It's made difficult as they don't care enough to simplify it. You may find it easy as you know the subject now but no one I showed it to was able to figure it out. Keep in mind induction is an easy topic to learn.

Random page I found with more complex problems:
View attachment 4907020View attachment 4907021

I'm buying this book. It's name?

 

[brotato78]

how it feels reading ts high iq thread

 

[topology]

I'm buying this book. It's name?

Number theory

George E. Andrews

 

[GuyFromSingapore]

@topology