Search found 151 matches
- Sun Dec 19, 2010 10:59 am
- Forum: National Math Olympiad (BdMO)
- Topic: The biggest value of k
- Replies: 15
- Views: 9523
Re: The biggest value of k
You precisely don't need to calculate the sum of the digits. If $0 \le k \le 2$ you can find it by simply evaluating the sum $19+20+...92$ which is $4278$ this is divisible by $3$ but not $9$. That makes the result being $1$
- Sat Dec 18, 2010 4:34 pm
- Forum: Secondary Level
- Topic: Can all the digits of a square be same?
- Replies: 6
- Views: 4830
Re: Can all the digits of a square be same?
There is nothing to be confused Masum, consider the available options for $a$ and u'll land safe
- Sat Dec 18, 2010 4:33 pm
- Forum: Divisional Math Olympiad
- Topic: A problem of Modular Arithmetic
- Replies: 9
- Views: 5786
Re: A problem of Modular Arithmetic
The numbers are of the form $60n+1$
There's no single residue when dividing by 7, can there be?
There's no single residue when dividing by 7, can there be?
- Fri Dec 17, 2010 9:45 pm
- Forum: Geometry
- Topic: Simple Proof of Pythagorean Theorem using Power of a Point
- Replies: 5
- Views: 3998
Simple Proof of Pythagorean Theorem using Power of a Point
চিত্রে ACO সমকোণী ত্রিভুজের O কে কেন্দ্র OA ব্যাসার্ধের করে একটি বৃত্ত আঁকা হয়েছে। GH হচ্ছে সেই বৃত্তের ব্যাস এবং AC কে B পর্যন্ত বর্ধিত করা হয়েছে। এক্ষেত্রে C, AB এর মধ্যবিন্দু হবে। পাওয়ার অফ পয়েন্টের ধারণা থেকে আমরা লিখতে পারি, $AC.CB = GC.CH$ Hence, $AC^2 + CO^2 $ $= GC.CH + CO^2$ $ = CO.(GC ...
- Fri Dec 17, 2010 11:18 am
- Forum: Secondary Level
- Topic: Can all the digits of a square be same?
- Replies: 6
- Views: 4830
Can all the digits of a square be same?
Is there any non-trivial square (having multiple digits) all of whose digits are same??
Hint:
Hint:
- Fri Dec 17, 2010 11:07 am
- Forum: Secondary Level
- Topic: Inequalities
- Replies: 6
- Views: 4708
Re: Inequalities
the terms $min(a,b)$ and $max(a,b)$ represent the minimum and maximum of $a$ and $b$ respectively.
Take an example:
$min(3,4)=3$
and $max(3,4)=4$
Take an example:
$min(3,4)=3$
and $max(3,4)=4$
- Fri Dec 17, 2010 11:04 am
- Forum: Secondary Level
- Topic: Find maximum value
- Replies: 7
- Views: 5269
Re: Find maximum value
The trick is to realize that irrespective of the choice of $x$ or $p$, the given expression can be rewritten as:
$(x-p)+(15-x)+(15-(x-p))$
the rest is simple
$(x-p)+(15-x)+(15-(x-p))$
the rest is simple
- Wed Dec 15, 2010 12:13 am
- Forum: Junior Level
- Topic: When the sum is a prime
- Replies: 5
- Views: 4498
When the sum is a prime
It should be trivial but I just found it today
If sum of two positive integers $a$ and $b$ is a prime then $a$ and $b$ are mutually coprime.
If sum of two positive integers $a$ and $b$ is a prime then $a$ and $b$ are mutually coprime.
- Wed Dec 15, 2010 12:10 am
- Forum: Junior Level
- Topic: Divisible by 169
- Replies: 6
- Views: 5096
Re: Divisible by 169
didn't try, but induction should work
- Tue Dec 14, 2010 12:52 am
- Forum: Asian Pacific Math Olympiad (APMO)
- Topic: Easiest problem of Apmo
- Replies: 18
- Views: 12849
Re: Easiest problem of Apmo
I still don't prefer using difficulty denoting adjectives with problems...