Question 24
Determine, in each case, all real numbers $x$ such that:
$$
a) \lfloor x \rfloor + \lfloor 2x \rfloor + \dots + \lfloor 2012x \rfloor = 2013;
$$
$$
b) \lfloor x \rfloor + \lfloor 2x \rfloor + \dots + \lfloor 2013x \rfloor = 2014.
$$
$$
a) \lfloor x \rfloor + \lfloor 2x \rfloor + \dots + \lfloor 2012x \rfloor = 2013;
$$
$$
b) \lfloor x \rfloor + \lfloor 2x \rfloor + \dots + \lfloor 2013x \rfloor = 2014.
$$