I also disagree with my solution but still feel like I should be able to do something with set theory (I'm not well versed enough I think).
You documented your thinking really well. It was very easy to follow what you were thinking. It also showed the point where you tried something new (the same point I didn't) which allowed you to push through to the final answer. I wonder if this problem was more dificult than it seemed at first.
I liked your diagrams. I did the problem quite systematically and didn't document every thought I had. Maybe I should have, but we have different solutions. I had each person in the village having (n-1)C2 keys for the nC2 locks. Now I must relook at my solution.
Thank you for this! I was given this problem 15 years ago when I took a class for middle school math teachers. The teacher knew we were swamped with homework so he just asked us to "get it started." So it'd been on the back burner until I found it yesterday. Will not look at your solution above as I really want to spend time doing this myself. Great blog, btw!
As chance would have it, I received a question about the 'Sequence' problem from a 6th grade teacher in Winnipeg just a few days ago. That reminded me about Jacobean Locks which I had been thinking about about a year ago, and meant to return to it, but it had slipped my mind.
So I googled and found your blog. Excellent account of your thinking ... I broke off in order to think about it freshly for myself. I usually have to start from scratch every time I return to these problems!
Regards to Mike!
JohnM (Author of Thinking Mathematically) PS: have you seen the new edition? 70 new problems plus glossary of all problems and a new chapter on thinking about processes as natural powers every child possesses.
Hmm. . .is your answer the same as sum from 1 to n-1?
ReplyDeleteOh, I mean does everybody have n-1 keys?
ReplyDeleteI also disagree with my solution but still feel like I should be able to do something with set theory (I'm not well versed enough I think).
ReplyDeleteYou documented your thinking really well. It was very easy to follow what you were thinking. It also showed the point where you tried something new (the same point I didn't) which allowed you to push through to the final answer. I wonder if this problem was more dificult than it seemed at first.
I liked your diagrams. I did the problem quite systematically and didn't document every thought I had. Maybe I should have, but we have different solutions. I had each person in the village having (n-1)C2 keys for the nC2 locks. Now I must relook at my solution.
ReplyDeleteThank you for this! I was given this problem 15 years ago when I took a class for middle school math teachers. The teacher knew we were swamped with homework so he just asked us to "get it started." So it'd been on the back burner until I found it yesterday. Will not look at your solution above as I really want to spend time doing this myself. Great blog, btw!
ReplyDeleteFYI, I just googled the math professor, Mike Shaughnessy, who assigned this problem, is now the NCTM president, will be for next 2 years! Small world.
ReplyDeleteAs chance would have it, I received a question about the 'Sequence' problem from a 6th grade teacher in Winnipeg just a few days ago. That reminded me about Jacobean Locks which I had been thinking about about a year ago, and meant to return to it, but it had slipped my mind.
ReplyDeleteSo I googled and found your blog. Excellent account of your thinking ... I broke off in order to think about it freshly for myself. I usually have to start from scratch every time I return to these problems!
Regards to Mike!
JohnM (Author of Thinking Mathematically)
PS: have you seen the new edition? 70 new problems plus glossary of all problems and a new chapter on thinking about processes as natural powers every child possesses.