 ## 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…