An International Mathematical Olympiad level Number Theory problem.

A probability question from the Cambridge maths entrance exam.

A simultaneous equation from Putnam

Putnam is one of the most well known undergraduate maths competitions in the world. To some, it…

An elegant functional equation combined with an integral

A quick problem from the Oxford maths admission exam.

The problem is as follows. 
Take log(x) to be log base 10 rather than base 2 in this question. Given that log(2) = 0.3010 to 4 decimal places and that 10^(0.2) <2, find the first digit of 2¹⁰⁰ and its length.
Please note that these…

The most elegant inequality in Putnam.

Once more, we look at a problem from Putnam. However, this time it is a little bit different…

Digit counting problem from the Vojtěch Jarník international math competition.

A nice integral from the UK integration bee

With the UK integration bee passing recently, we have a multitude of new problems…

A derivative problem from Putnam

Once more, we are doing a Putnam problem, the competition many are too scared to attempt. This time…

A cute integral with the indicator function from the 2023 UK integration bee