Absolutely yes. I like games. The purpose of games is to have fun. This seems like a fun game for like the first $20, a sum I can afford to play a fun game for 10 minutes.
Then at the end, I get to say "I once lost $20 to Steve Balmer playing binary search", which is a fun sentence I can dine out on, and is worth more than $20 to me.
I feel like perhaps this is why MS under Balmer lost relevance. Too busy looking at the technical and not the human.
If you answered like this in an interview I would definitely not give you the job. I did actually interview someone once who was like this - "How would you do this?" "Well you shouldn't do it. I think you should do this other thing.". He did not get the job.
It's like interviewers don't understand the power dynamics going on during an interview: for the interviewer, this is just their job. Nothing will change for them whether they pass the candidate or not. This could be their 100th interview. On the other hand the interviewee is not paid to be there, they could be doing something else and they are stressed as who knows what kind of egocentric asshole might be interviewing them for a job they want.
If I get a candidate who can make a fun and clear headed remark in such a tense situation, I would read that as them being comfortable with problems and with stress. I would move forward and ask further questions to see their thought process but rejecting someone out of a single question is ludicrous.