In this problem set we present four questions:

**(Middle School Students)**

The irrational number is formed

by using alternating blocks of and zeros, where the th block

of zeros following the decimal contains zeros. What is the digit

in the 2550th place following the decimal?

**(High School Students)** Consider the function given by

Find the maximum and minimum value of the function.

**(Undergraduate Students)** Let be an infinitely differentiable function, such that

- whenever
- and where and is the -th derivative of

Let is given by

Decide whether is infinitely differentiable on .

**(Masters Students and above)** If is a measurable subset of such that

then has measure