Brain Teasers

[Gerald Higgins]

Not necessarily, a j can be considered an item by itself, but is composed of two items.

Much like a car is one item, but is made from many items.

Well this could debate could go on and on.
Yes of course, in the loosest sense, a car is one item, and each of it's components are also items.
As are the individual atoms of which the tyres, wiper blades and so on, are made.
Applying your logic to this puzzle, you could choose to describe a group of any 2 or more j's in this puzzle as "an item", in which case solving the problem becomes trivial.

Reading Sandeep's later posts, I think it's clear he didn't intend that kind of interpretation.

 

[Oaktree]

IMO, 10 queens on a 10x10 board is a lot easier than 8 queens on an 8x8 board.

Here's a solution for the 10 queens:

Book2
	A	B	C	D	E	F	G	H	I	J
1						6
2	1
3							7
4		2
5								8
6			3
7									9
8				4
9										10
10					5
Sheet1

 

[mikerickson]

Here is a conundrum.

You walk one mile south, one mile east and one mile north.
After this three mile walk, you end up back where you started.

Your journey might have begun at the North Pole.

What other place on the earth might you have started from?

 

[Gerald Higgins]

Mike - I believe there are theoretically an infinite number of locations that fit that bill, and for practical purposes there are many, although they're all pretty close to each other (without wishing to give it away). Am I right ?

 

[mikerickson]

Gerald, I sounds like you've got it.

 

[Scott Huish]

Although theoretically you would end up where you started, i.e. the North Pole, given that description, you can't possibly end up where you started exactly. You would have to walk approximately 1.4 miles northwest back to do that. (a squared + b squared = c squared) So as long as you are in the same place and a mile away is still in the same place (i.e. the same country for example), you could do this almost anywhere except where a mile away from any point in the journey puts you in a different city or country for example.

 

[lenze]

I think Gerald is on the right track! There are an INFINITE number of places you could start!!
lenze

 

[Aaron.B]

I'm going with the south pole.

The globe is not a plane.

 

[pgc01]

I also see a 2 * infinite number of locations where you could start your trip. By a 2 * infinite I mean an infinite number of longitude values (any value) * an infinite number of latitude values (an infinite series of values).

BTW, I tried (not manually) all the possible solutions for the 10 queen problem and found 724 different solutions.

 

[mikerickson]

HotPepper, starting from the North pole, one would get back to the North Pole, exactly. Pythagorean theorm only works on the plane. The sum of the angles of any triangle on a spherical surphace is greater than 180.

Aaron, If one is standing on the South Pole, how does one make the first leg of the journey, "walk 1 mile south"?

PGC, one could look at it that, given any positive integer N, there is an uncountably infinite set of solutions associated with N.
(Count of solutions) = (Count of Integers)*(Count of Real numbers >0 and <1)