Problem of the Week (23rd May, 2022)
Let be the smallest integer for which has 2016 digits.What is the units digit of ? Source: Senior Maths Challenge, 2016…
Problem of the Week (16th May, 2022)
Consider triangle with side lengths , , and . Let be the midpoint of segment , and let be the point on the interior of segment that also…
Problem of the Week (9th May, 2022)
The area of the region bounded by the graph of is , where and are integers. What is ? Source:…
Problem of the Week (2nd May, 2022)
In a cyclic quadrilateral , the lengths of the sides , , and are in arithmetic progression with common difference . If angle is degrees,…
Problem of the Week (14th Mar, 2022)
For natural number , define the function to be the number you get by adding the digits of the number . For…
Problem of the Week (7th Mar, 2022)
Define the function by where , and otherwise. The sum of all real numbers for which can be written as…
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 (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…