One of the favorite problems that I assigned to my students was the New Year problem. I first read about it in the Mathematics Teacher in the 1960's. I assigned the problem every year before the Christmas break from 1968 to 1999.
The object is to form expressions for all the positive integers from 1 to 99 using in order the four digits of the New Year and the operations addition, subtraction, division, multiplication, square root, exponentiation, factorial, and the greatest integer function. Parentheses may also be used.
I found that many of my students enjoyed this problem because it allowed them to be creative in their solutions.
Click here for examples of previous years