The problem simply states that:

show that there cannot be 171 binary sequences such that each differ in at least four digits.

So far I've deducted that there should be some pigeonhole principle in here (I'm assuming, at least). So far I've written down that we should take the 2^12 different sequences and subtract the ones which only differ by one and those that differ only by two and then by three. I've tried this but with little success. Could I please have some guidance on how to go about this question?

thank you