What is the value of \(\left(2^{0}-1+5^{2}+0\right)^{-1}\times 5\)?
A box contains a collection of triangular and square tiles. There are 25 tiles in the box, containing 84 edges total. How many square tiles are there in the box?
Ann made a 3-step staircase using 18 toothpicks as shown in the figure. How many toothpicks does she need to add to complete a 5-step staircase?
Pablo, Sofia, and Mia got some candy eggs at a party. Pablo had three times as many eggs as Sofia, and Sofia had twice as many eggs as Mia. Pablo decides to give some of his eggs to Sofia and Mia so that all three will have the same number of eggs. What fraction of his eggs should Pablo give to Sofia?
Mr. Patrick teaches math to 15 students. He was grading tests and found that when he graded everyone's test except Payton's, the average grade for the class was 80. After he graded Payton's test, the class average became 81. What was Payton's score on the test?
The sum of two positive numbers is 5 times their difference. What is the ratio of the larger number to the smaller?
How many terms are there in the arithmetic sequence \(13,16,19,\ldots,70,73\)?
Two years ago Pete was three times as old as his cousin Claire. Two years before that, Pete was four times as old as Claire. In how many years will the ratio of their ages be \(2:1\)?
Two right circular cylinders have the same volume. The radius of the second cylinder is \(10%\) more than the radius of the first. What is the relationship between the heights of the two cylinders?
How many rearrangements of \(abcd\) are there in which no two adjacent letters are also adjacent letters in the alphabet? For example, no such rearrangements could include either \(ab\) or \(ba\).
The ratio of the length to the width of a rectangle is \(4:3\). If the rectangle has diagonal of length \(d\), then the area may be expressed as \(kd^{2}\) for some constant \(k\). What is \(k\)?
Points \((\sqrt{\pi},a)\) and \((\sqrt{\pi},b)\) are distinct points on the graph of \(y^{2}+x^{4}=2x^{2}y+1\). What is \(|a-b|\)?
Claudia has 12 coins, each of which is a 5-cent coin or a 10-cent coin. There are exactly 17 different values that can be obtained as combinations of one or more of her coins. How many 10-cent coins does Claudia have?
The diagram below shows the circular face of a clock with radius 20 cm and a circular disk with radius 10 cm externally tangent to the clock face at 12 o'clock. The disk has an arrow painted on it, initially pointing in the upward vertical direction. Let the disk roll clockwise around the clock face. At what point on the clock face will the disk be tangent when the arrow is next pointing in the upward vertical direction?
Consider the set of all fractions \(\frac{x}{y}\), where \(x\) and \(y\) are relatively prime positive integers. How many of these fractions have the property that if both numerator and denominator are increased by 1, the value of the fraction is increased by \(10%\)?
If \(y+4=(x-2)^{2}\), \(x+4=(y-2)^{2}\), and \(x\neq y\), what is the value of \(x^{2}+y^{2}\)?
A line that passes through the origin intersects both the line \(x=1\) and the line \(y=1+\frac{\sqrt{3}}{3}x\). The three lines create an equilateral triangle. What is the perimeter of the triangle?
Hexadecimal (base-16) numbers are written using numeric digits 0 through 9 as well as the letters \(A\) through \(F\) to represent 10 through 15. Among the first 1000 positive integers, there are \(n\) whose hexadecimal representation contains only numeric digits. What is the sum of the digits of \(n\)?
The isosceles right triangle \(ABC\) has right angle at \(C\) and area 12.5. The rays trisecting \(\angle ACB\) intersect \(AB\) at \(D\) and \(E\). What is the area of \(\triangle CDE\)?
A rectangle has area \(A\text{ cm}^{2}\) and perimeter \(P\text{ cm}\), where \(A\) and \(P\) are positive integers. Which of the following numbers cannot equal \(A+P\)?
Tetrahedron \(ABCD\) has \(AB=5\), \(AC=3\), \(BC=4\), \(BD=4\), \(AD=3\), and \(CD=\frac{12}{5}\sqrt{2}\). What is the volume of the tetrahedron?
Eight people are sitting around a circular table, each holding a fair coin. All eight people flip their coins and those who flip heads stand while those who flip tails remain seated. What is the probability that no two adjacent people will stand?
The zeroes of the function \(f(x)=x^{2}-ax+2a\) are integers. What is the sum of all possible values of \(a\)?
For some positive integers \(p\), there is a quadrilateral \(ABCD\) with positive integer side lengths, perimeter \(p\), right angles at \(B\) and \(C\), \(AB=2\), and \(CD=AD\). How many different values of \(p<2015\) are possible?
Let \(S\) be a square of side length 1. Two points are chosen independently at random on the sides of \(S\). The probability that the straight-line distance between the points is at least \(\frac{1}{2}\) is \(\frac{a-b\pi}{c}\), where \(a\), \(b\), and \(c\) are positive integers and \(\gcd(a,b,c)=1\). What is \(a+b+c\)?
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.
Cheenta students shine at the Purple Comet Math Meet 2025 organized by Titu Andreescu and Jonathan Kanewith top national and global ranks.
Celebrate the success of Cheenta students in the Stanford Math Tournament. The Unified Vectors team achieved Top 20 in the Team Round.