Knights Templar Maths Quest

In preparing for my math travels I did a lot of "digging" - looking for anything and everything math-related in each place I was going.  Earlier today I took in a math lecture at the Museum of London put on by Gresham College, which has been presenting free lectures in London for over 400 years.  That's quite a tradition!  The lecture was on John von Neumann and Alan Turing - their contributions to the war effort in WWII and their ongoing contributions, a nice parallel biography.  Gresham Professor of Geometry, Raymond Flood, did an excellent job with this presentation.

Tonight was just a ton of fun!  It was a lot like the tutor trainings I've run at MJC (how's that for self-promotion?), but I was a participant and not the leader, so it was my turn to be the solver and to work in things in real-time instead of having worked the out on my own ahead of time.  It was an eclectic mix of people, and a lot of them!

I can't remember at this point how I came across MathsJam, but it was a good find.  It's a world-wide maths event that takes place on the second-to-last Tuesday of every month.  In places where it is held, people gather in pubs and bring fun math stuff to do together.  Here's their website: http://www.mathsjam.com/

I've included so many pictures of people at this event (and please know there were more tables of people involved in this that I didn't get pictures of) to show that math can be a fun and social event.  These people are gathered here on a Tuesday night to do maths together - people from all walks of life who simply like puzzles.  I've heard people say so often, "I'm a people person, not a math person."  It is so OK to not be into math - all of us like certain things and not other things - but as a society we need to quit propagating the idea that being a "people person" and being a "math person" are mutually exclusive.  If we keep promoting that false dichotomy as a society we send a terrible message to our young people who, if they think it's uncool, might not give math a chance - when it could be something they would enjoy and could be something that could open doors to careers for them.  Like math, dislike math, whatever - but don't send the message to our youth that math is uncool or unsocial, because that is simply false.  (rant over)

 I want to close with some problems in case you'd like to get involved and go on a maths quest of your own!  I have pictures of two of them and have listed some others for your solving pleasure :-)

1)

2) Fill in the blanks to make a true equation: 1  2  3  4  5  6  7  8  9  10 = 2016.  (You are allowed fill in the blanks with any mathematical operations or symbols; there are multiple answers.)

3)  Find a set of four numbers such that the greatest common divisor of any three of them is 1, but the greatest common divisor of any two of them is greater than 1.

4)  On the chalkboard are written 1!, 2!, 3!,  .  .  .  100!.  Is it possible to erase one of these so that the product of the remaining numbers is a perfect square?

5) See "Prove" below: