# Rambling puzzles…Number plates, shoelaces and you.

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Mr Smith has 8 children, and each one is a different age. His entire family is in the car, when his eldest, aged 9, shouts out “Daddy! That number plate has only two numbers, and each number is repeated twice! And the number is divisible by each of our ages!” “You’re Correct!” Mr Smith shouts as he whips out his iPhone to check. “and look, the last two digits are my age!”

What is Mr Smith’s age?Actually the question wasn’t like that, it gave you choices and you had  to say which of those numbers were not the age of one of his kids, but this question is a bit harder and more interesting.
The second question:there are 30 shoelaces in a closed box with all of their ends sticking out (so 60 ends). You tie one end to another, and keep doing this until each end is connected to one other.
How many ways are there of doing this?
What is the expected numberof loops?This was on the “Mind Your Decisions” Blog, and I gave a comment which got beautifully shot down by a fellow commentator, And I’m still uncertain who was right.
But anywho, have a go at the puzzles and see if you can solve them.
The first question I don’t know if it’s possible to answer without extra info. If it isn’t, try work out what extra info you need.
As for the second, the only decent suggestion I have is you start with a smaller number and see what happens.
I also recently discovered that Cambridge University has a very different teaching approach to mathematics. They arrange for 2 students to meet up with a lecturer to go over mathematics that they’ve been doing. I’m quite jealous of this! And yet I wonder if I’d actually take the opportunity…doubtless there are people somewhere who will hear about Auckland University and be amazed I haven’t taken more opportunities that have been offered to me, yet from my point of view, they don’t seem like options.
One thing I’ve always been told to do is go and speak to my lecturers. (In fact, I’ve told people to do it myself). Yet I never have. I always think “what would I talk to them about?” I have one query for one of my lecturers, but it seems incredibly trivial and it has no point other than to give me something to talk about with him for about 43 seconds (it takes about 13 seconds to say hello, how are you etc normally). And then? Do I just leave or what? This is why I would like the chance to have a supervisor, but the truth is I do have the chance, I’m just not taking it.I was aiming to speak to one of my lecturers this last week, but have been unable to attend uni this last week and a half…so I think I’m going to aim to go and speak to some of them next week. With some good questions. Hopefully.
I’ve been reading a fair amount of mathematics recently,online and print, about mathematics and mathematicians. There are a variety of mathematicians, some are ‘gifted’ (or ‘genius’) and others persevere and work hard at it – and of course there are varying degrees of both in some mathematicians, and some great mathematicians have neither. But no matter what ‘category’the mathematician falls into, one key characteristic is passion, passion for mathematics. Another, a willingness to forge a new path that no ones been down before.
It is this second that strikes me most. Too often we do what we are expected to do, and not what we want to do. The joy is doing what we want. If we feel forced into doing it, there is not much joy there.
Some mathematicians will tell you to memorise important theorems and proofs – that is the way to be a good mathematician. Others will tell you to discover the proofs and theorems yourself – that is the way to be a good mathematician. And yet others will tell you find a good mathematician and be their ‘apprentice’ – that is the way to be a good mathematician.
But I guess it all comes down to us as individuals. What do you want to do? How do you want to do it? Forget about the marks or opinions,what do you want to do?