 ## Problem of the Week (28th Feb, 2022)

The sequence  can be abbreviated as . You are given that is an arithmetic progression with first term  and common difference   is an… ## Problem of the Week (21st Feb, 2022)

Let , where are complex numbers. Suppose that . What is the number of non-real zeros of ? Source: AMC… ## Problem of the Week (14th Feb, 2022)

How many subsets of  contain exactly one prime number? Source: Purple Comet Math Meet, High School Round, 2014 Happy problem solving! … ## Problem of the Week (7th Feb, 2022)

Mary has a sequence , such that for each ,  is the least positive integer  for which none of the base- logarithms are integers. Find… ## Problem of the Week (31st Jan, 2022)

Convex quadrilateral has , . Diagonals and intersect at , and . have equal areas. What is the length of… ## Problem of the Week (24th Jan, 2022)

Imagine cutting a spherical loaf of bread into parallel slices with equal width. What fraction of the total surface area… ## Problem of the Week (17th Jan, 2022)

The positive integers  are the smallest that satisfy the equations: If , where  and  are positive integers, then what is ? Source: Ritangle, Stage 1,… ## Problem of the Week (10th January, 2022)

There are 8 lily pads in a pond numbered 1,2,…,8. A frog starts on lily pad 1. During the -th second,… ## Problem of the Week (13th December, 2021)

You have a sphere, the points on the surface of which can be colored white or black. You are told… ## Problem of the Week (6th December, 2021)

Given an infinite lattice of points, colored with 5 colors, prove that it is always possible to find a monochromatic…