Find the number of 8 digit numbers sum of whose digits is 4. Discussion: Suppose the number is $latex a_1 a_2 a_3 ... a_8 $.The possible values of $latex a_1 $ are 1, 2, 3, 4. We consider these four cases. If $latex a_1 = 4 $ then all other digits are 0 (since sum […]
In this post, there are questions from Regional Math Olympiad 2013. Try out the problems. Find the number of 8 digit numbers sum of whose digits are 4.Discussion Find the number of 4-tuples (a,b,c,d) of natural numbers with $latex a \le b \le c $ and $latex a! + b! + c! = 3^d […]
"How do I involve my child in challenging mathematics? He gets good marks in school tests but I think he is smarter than school curriculum." "My daughter is in 4th grade. What competitions in mathematics and science can she participate in? How do I help her to perform well in those competitions?" "I have a […]
In math olympiads around the world, number theory problems have many recurring themes. One such theme is the 'LTE' or lifting the exponent. Selective Logarithm We define a function callled Selective Logarithm (SL) which works on all integers (positive, negative or zero). Suppose N is any integer and p be a prime then $latex SL_p […]
Let's discuss a problem based on Arithmetic of Remainders and understand the concept behind it. Consider the two number: 37 and 52 What is the remainder when we divide 37 by 7? 2 of course. And 52 produces remainder 3 when divided by 7. Suppose we want to know the remainder when the product of […]
Let's understand one-one function and differentiability with the help of a problem. Try it yourself before reading the solution. Let f be real valued, differentiable on (a, b) and $ f'(x) \ne 0 $ for all $ x \in (a, b) $. Then f is 1-1. True Discussion: Suppose f is not 1-1. Then there […]
Lets understand direct product of two subgroups with the help of a problem. This problem is useful for College Mathematics.
What is RMO? RMO or Regional Math Olympiad is the second round of Mathematics Contest in India after the Pre-regional Mathematics Olympiad (Pre-RMO or PRMO) leading to the prestigious International Mathematics Olympiad (IMO). It is held in the month of December (the first Sunday of December). The test is conducted in each of the 19 […]
Let's understand Fixed Point of continuous bounded function with the help of a problem. This problem is useful for College Mathematics.