Brain Teaser No 1
Posted by: Don Atkinson on 16 November 2001
THE EXPLORER
An explorer set off on a journey. He walked a mile south, a mile east and a mile north. At this point he was back at his start. Where on earth was his starting point? OK, other than the North Pole, which is pretty obvious, where else could he have started this journey?
Cheers
Don
Posted on: 19 May 2003 by Matthew T
Don,
Not long, less then a mintue I would think.
The paper version was to explain how I got there.
Matthew
Not long, less then a mintue I would think.
The paper version was to explain how I got there.
Matthew
Posted on: 19 May 2003 by Don Atkinson
Not long, less then a mintue I would think.
Sorry about this Matthew............
however......
Another 'in-the-head' one (ie trivial)
At an exclusive ball for canadian Naim Dealers and thier customers, the total amount taken in ticket sales was $Canadian 9,540.00
(I am using $Canadian to make our friends across the water feel included)
The attendance was between 70 and 100 and each person (including the dealers) paid exactly the same amount in whole dollars only.
How much was each ticket?
Matthew, you can of course
Sorry about this Matthew............
however......
Another 'in-the-head' one (ie trivial)
At an exclusive ball for canadian Naim Dealers and thier customers, the total amount taken in ticket sales was $Canadian 9,540.00
(I am using $Canadian to make our friends across the water feel included)
The attendance was between 70 and 100 and each person (including the dealers) paid exactly the same amount in whole dollars only.
How much was each ticket?
Matthew, you can of course
Posted on: 19 May 2003 by Don Atkinson
Ooops,
computerscreen froze....
Matthew, you can of course write the answer down and even the explanation.....
cheers
Don
computerscreen froze....
Matthew, you can of course write the answer down and even the explanation.....
cheers
Don
Posted on: 19 May 2003 by Paul Ranson
106CDN
(54 looks like a multiple of 9, so does 9. I was never good at tables by a few numbers remain familiar. I always used to have to work things out.)
Paul
(54 looks like a multiple of 9, so does 9. I was never good at tables by a few numbers remain familiar. I always used to have to work things out.)
Paul
Posted on: 21 May 2003 by Matthew T
Paul seemed to have hit the nail on the head.
Matthew
Matthew
Posted on: 27 May 2003 by Don Atkinson
Paul, Matthew,
Yes, head, nail, hit....
Cheers
Don
Yes, head, nail, hit....
Cheers
Don
Posted on: 27 May 2003 by Don Atkinson
The Carpenters
Take a perfect wooden cube.
You have to find a way to saw through it in one single straight cut which divides it so as to produce two perfectly hexagonal surfaces with no messing.
Cheers
Don
Take a perfect wooden cube.
You have to find a way to saw through it in one single straight cut which divides it so as to produce two perfectly hexagonal surfaces with no messing.
Cheers
Don
Posted on: 27 May 2003 by Paul Ranson
That's quite cool. But I've got no idea how to describe it.
Paul
Paul
Posted on: 28 May 2003 by Matthew T
Does this make sense.
Matthew
Matthew
Posted on: 28 May 2003 by Paul Ranson
Exactly.
We need six sides to our face, so the cut must pass through all 6 faces of the cube. All the sides of the hexagon are of similar length, which I think implies that the cut passes through the midpoints of the appropriate edges.
Paul
We need six sides to our face, so the cut must pass through all 6 faces of the cube. All the sides of the hexagon are of similar length, which I think implies that the cut passes through the midpoints of the appropriate edges.
Paul
Posted on: 28 May 2003 by Don Atkinson
All the sides of the hexagon are of similar length,
All the sides of a hexagon are of EQUAL length.
In Matthew's picture (nice one Matthew) if the cube side is 2L then the hexagon side will be L(sqrt2)
Cheers
Don
All the sides of a hexagon are of EQUAL length.
In Matthew's picture (nice one Matthew) if the cube side is 2L then the hexagon side will be L(sqrt2)
Cheers
Don
Posted on: 28 May 2003 by Don Atkinson
The same picture as Mathew's but from a different angle......
Cheers
Don
Cheers
Don
Posted on: 28 May 2003 by Paul Ranson
quote:
All the sides of a hexagon are of EQUAL length.
When I'm wielding the inappropriate saw then 'similar' is the best you can hope for.
Paul
Posted on: 31 May 2003 by Don Atkinson
When I'm wielding the inappropriate saw then 'similar' is the best you can hope for.
Whilst your in this sabre rattling mood, how about slicing a tetrahedron to reveal a perfect square, no messing about.
Cheers
Don
Whilst your in this sabre rattling mood, how about slicing a tetrahedron to reveal a perfect square, no messing about.
Cheers
Don
Posted on: 02 June 2003 by Matthew T
Well, if you chop it in half and leave two identical pieces you would find that they both have a square face!
Matthew
Matthew
Posted on: 02 June 2003 by Don Atkinson
Matthew,
Yes!
Some readers might have difficulty visualising chopping a tetrahedron in half so as to form two identical pieces.
Its a long time since we had frozen Jublies!
Cheers
Don
Yes!
Some readers might have difficulty visualising chopping a tetrahedron in half so as to form two identical pieces.
Its a long time since we had frozen Jublies!
Cheers
Don
Posted on: 02 June 2003 by Paul Ranson
Surely there are two ways to split a tetrahedron in two? One gives you two now irregular tetrahedra, the other gives you the square face.
Paul
Paul
Posted on: 03 June 2003 by Matthew T
But Paul, are those irregular tetrahedron identical?
Matthew
Matthew
Posted on: 03 June 2003 by Paul Ranson
I believe so.
Paul
Paul
Posted on: 03 June 2003 by Matthew T
Paul,
The halves that give a square are as indicated on the left below. The halves I think you mean are indicated on the right and are no identical but are mirror images of each other.
Matthew
The halves that give a square are as indicated on the left below. The halves I think you mean are indicated on the right and are no identical but are mirror images of each other.
Matthew
Posted on: 03 June 2003 by Paul Ranson
I wonder what 'identical' really means?
But I take your point. Which is left and which is right?
Paul
But I take your point. Which is left and which is right?
Paul
Posted on: 03 June 2003 by Don Atkinson
Paul,
Identical=no differences=absolute sameness
But not 'one and the same'
possibly....
Cheers
Don
Identical=no differences=absolute sameness
But not 'one and the same'
possibly....
Cheers
Don
Posted on: 03 June 2003 by Don Atkinson
My tetrahedron,
....well I had drawn it so I might as well post it....
Cheers
Don
....well I had drawn it so I might as well post it....
Cheers
Don
Posted on: 03 June 2003 by Don Atkinson
Well, obviously (for Paul's sake) the two halves do not have identical orientations and they can never occupy identical positions simultaneously.....but for all practical purposes......they are identical.....
Cheers
Don
Cheers
Don
Posted on: 03 June 2003 by Paul Ranson
Interestingly the square halves as well as being identical are similar in the same way that the triangular halves are...
Paul
Paul