$A$ tells $B$ : "I could be visiting you on any day in the next two months and you must give me gold coins of as much total weight in grams as the number of days that would elapse from today." If gold coins are available in integer gram weights, what is the least number of coins with which $B$ can meet $A$'s demand on any day?
$(1)$ $31$
$(2)$ $7$
$(3)$ $6$
$(4)$ $13$
How to approach this problem? Can anybody shed some light on it? Thanks for your time.
Source $:$ CSIR NTA NET DECEMBER $2019.$
Hint :
Any positive integer can be written as sum of powers of $2$. Every decimal number has a (unique) binary (base-$2$) representation.