MathsEconomics:
General problem:

Darivie04:

Seems straightforward...

Darivie04:

I know the answer to this as an identity.

MathsEconomics:


What's straightforward? Finding the range of expressions is never a straightforward task, however, I'll like to see your "straightforward" approach.

Darivie04:

All combinations of a and b constitutes the function's domain. Knowing that, its clear to find its range.

MathsEconomics:


Range is quite different from domain, note also domain D of a function is the subset D of real numbers for which that particular function is defined.

To find domain, all you need to study is study the function and determine the set of n-tuples of Real numbers for which that function is meaningless.

On the other hand, to find the range, it suffices to study the function analytically, using several tools from Algebra to find the extremal values of the function concerned and prove that for am appropriate n-tuple such extremal values are possible.

Range is a more difficult task.

Darivie04:
General Problem:
Prove that there is no power of 2 that when you rearrange its digits forms another power of 2.

MathsEconomics:
I decided to type my solution.

MathsEconomics:
I gave this problem to my students in ss1 as assignment.

The number 3.15, it's integer part is 3 and it's fractional part is 0.15, use this knowledge to solve the given problem. (For Everyone).

Darivie04:


Your right that its not possible but the proof is wrong at the part when you say the permutations of a power of 2 are even.
Counterexample:
2^9=512 but 521 isn't even.

Darivie04:
Please can anyone suggest an introductory text for combinatorial geometry?

Darivie04:


I got 26.43 but I approximated a lot. I think the answer is 26.

MathsEconomics:


No, there's no error in my proof. I assumed that B must be even, there are many possible ways to permute a power of 2, but out of those possibilities, we only need to consider the case where the given permutation results to an even number.
We are asked to find a power of 2 from which the digits we get from the permutation of its digits is also a power of 2, clearly this given digit we get from the permutation can never be odd since if it was odd, it cannot never be a power of 2 since all powers of 2 are even.
So there is no loss in generality in assuming that the given number B must be even.

MathsEconomics:

I can send you good books on this subject. However, it's prerequisites are quite great.

Darivie04:


The two books I have on the topic have references to abstract algebra and analysis which I haven't yet studied. One of them is "Excursion into Combinatorial Geometry" and the other one was partly written by Pankaj K. Agarwal. Both of them seem like advanced books on the topic cause they both lack definitions and introductions to foremost things like a convex hull, which I assume to be one of the most basic concepts are missing from this books.

So I would really like to see your books but I lack a lot of prerequisites.

WinningEleven:

I've never seen this kind of maths all my life
What sorcery is this?

MathsEconomics:


I think those books are graduate level books as Abstract Algebra and Real Analysis are not prerequisites for the Olympiad.

Don't try to delve into Combinatorial Geometry now, first of all try to cover Combinatorics, Graph Theory, Algebra and Geometry and make sure you're comfortable with them before delving into monsters like
Combinatorial Geometry
Combinatorial Number Theory
Combinatorial Game Theory.


Note, these are also Olympiad topics.

MathsEconomics:


I think those books are graduate level books as Abstract Algebra and Real Analysis are not prerequisites for the Olympiad.

Don't try to delve into Combinatorial Geometry now, first of all try to cover Combinatorics, Graph Theory, Algebra and Geometry and make sure you're comfortable with them before delving into monsters like
Combinatorial Geometry
Combinatorial Number Theory
Combinatorial Game Theory.


Note, these are also Olympiad topics.

OrestesDante:



★ ★ ★ ★ ★ ★ ★ ★ ★ ★


∆ Help a soul..... Most of these stuffs are extremely time consuming... Also, there are lots and lots of branches in mathematics.... tons of them I don't which to delve into... I need to go into programming.... ASAP ∆


★ ★ ★ ★ ★ ★ ★ ★ ★ ★

MathsEconomics:
General Problem
Difficulty level: SS2
Topic: Number Theory.

Darivie04:


This is real math. Most of the math done from sec school just involves applying repetitive procedures or formulas which isn't really math. And even if in some sense it is, it doesn't really show the essence of math which is thinking and creativity.

Darivie04:


I didn't find it cheap sha probably because I'm still learning. Our poor standing in the IMO can be attributed to many things. Math is our country is majorly centered on speed and doesn't encourage anything outside the mainstream school math syllabus. Cowbellpedia isn't helping matters. Its sad to say its the prominent math competition in our country. When I talk to my fellow math inclined classmates they are usually preparing for Cowbellpedia and see Olympiads as "its not part of our syllabus". So when our most popular math competition Cowbell is mediocre our students too will be mediocre cause of course why do I have to crack my brain with olympiad math when they can possibly get millions from Cowbell which only requires me to answer easy questions in a short amount of time.

Meanwhile in US they have MATHCOUNTS which is for middle school(junior secondary) that asks tougher questions than senior section of Cowbell. Its clear why these countries outperform us in on the international
stage.

I also attribute a lot of the cause of our bad performance in IMO to the type of teachers we have here in Nigeria.