The year 1978 is such that the sum of the first two digits and the latter two digits is equal to the middle two digits, i.e. 19 + 78 = 97. What is the next year (after 1978) for which this is true?
There are multiple ways to solve the problem, as demonstrated here:
By the way, I am the person (formerly) at UBS who posed this question in an interview in mid-2010, as mentioned in the original post on quantnet; however the question was not to come up with a formula per se to find such years, but rather to say what is the next year without arriving at it merely by brute force. To my knowledge, apart from using brute force, one can solve the problem algebraically or via modular arithmetic, as described in the solutions posted on quantnet. Some people have solved it by simply "seeing" the answer, using neither algebra nor modular arithmetic, as I did in 2009 when I was asked this question during a phone interview and had no pen & paper in hand; one could argue that the "seeing" method is just mental brute force.