199 replies to this topic

[Time Out]

Spoiler for ?anagram

logistics

off to find a checker board

[fabpig]

Spoiler for Never thought

about anagramising.... nicely, Timey.... If it isn't, then another possibilty is GILD'S TIN(S).

I managed to get 13 on the chessboard. See what T.O. comes up with before I show the diagram and make a complete fool of myself....

[Yoruichi-san]

When I woke up, my brain started working again...

Spoiler for Oops...

Actually, ignore what I said the first time, I forgot to take into account the boundaries, which would divide the span into two moves, taking away the threat, I think. I'm not really a chess player.

it should be 13, as fabpig said. To minimize the number of squares you span with each bishop, put them as close to each other as possible, and move along the outside edge.

Is it just me, or do you start to see 8-dimensional vector spaces in everything when you're sleepy? *whistling*

[fabpig]

When I woke up, my brain started working again...

Spoiler for Oops...

Actually, ignore what I said the first time, I forgot to take into account the boundaries, which would divide the span into two moves, taking away the threat, I think. I'm not really a chess player.

it should be 13, as fabpig said. To minimize the number of squares you span with each bishop, put them as close to each other as possible, and move along the outside edge.

Is it just me, or do you start to see 8-dimensional vector spaces in everything when you're sleepy? *whistling*

it's just you.

Spoiler for Anyway, buoyed by the backup of Y-San, this is what I got:

Is there any relevance in the board being 90 degrees 'out'

Edited by fabpig, 14 May 2012 - 01:16 AM.

[Yoruichi-san]

it's just you.

Spoiler for Anyway, buoyed by the backup of Y-San, this is what I got:

Is there any relevance in the board being 90 degrees 'out'

Hmm...I'm having trouble seeing the picture, but I think you and I probably have something similar. Good job finding it first . I'm not sure what method you used, but since I like speaking math...well...

Spoiler for An alternative method of construction

Ignoring the "moves like a king" for now, if you place a bishop on the edge (i.e. minimum distance to edge = 0), it will only diagonally span (by which I mean cover, or be able to reach in one move and therefore eliminate as a placement point) 7 other squares, for a total of 8 squares. If you put with a minimum distance of 1 square from the edge, it will span 10, 2 will span 12, 3 will span 14. You want to minimize the number of squares that are eliminated as possible bishop placement squares, since you want to maximize the number of bishops placed. So choose one edge square (I started with a corner square) and place a bishop on it.

Now in order to minimize the number of squares covered, choose a square whose span includes the maximum number of squares already covered. That is, you want to eliminate as few additional squares as possible. In this case, one square is covered by both the first and second bishops, causing the second bishop to eliminate 7 additional squares from bishop placement. Now continue this trend of choosing squares whose span covers the maximum number of squares already covered, thereby eliminating the fewest additional squares. Depending on where you placed the second bishop, the remaining number of spaces eliminated will either be in the pattern (6,5,4,2,1) or (5,5,3,3,1). In either case, we now have a total of 32 out of 64 squares spanned/eliminated, all of one color square, which ever color you started with, and have placed 7 bishops, on opposite sides of the board.

Now repeat with the other color, on the other two sides, taking into account the "moves like a king" rule. The pattern for number spanned is (8,7,5,5,3), which gives you an additional 28 squares eliminated, for a total of 60, and you have placed 5 additional bishops, for a total of 12. Now you are left with 4 squares, 3 of which are eliminated due to the "moves like a king" rule, so you can place 1 last bishop in the remaining space, for a total of 13.

Consequently, without the "moves like a king" rule, you could place 14. But I think the thirteenth witch likes the number 13 for some reason...

Edited by Yoruichi-san, 14 May 2012 - 02:06 AM.

[fabpig]

What skullduggery - nay, witchcraft, is this? My beautiful picture vanish-ed while I was sleeping...

Spoiler for Oh well, we'll have another go

[Time Out]

A Witch in a chess game’s a powerful thing;
It can move like a bishop or move like a king.
So how many Witches, one way or another,
Can fit on this board without threatening each other?
I thought fabpig and Y- san were correct with 13, but no reply is forthcoming.
So for another tack.

Spoiler for ?Moves like a King

16

[WitchOfSecrets]

(I will try to post tonight or tomorrow - lots of work to do! The chess riddle is solved, but one remains.)

Edited by WitchOfSecrets, 15 May 2012 - 01:08 AM.

[Yoruichi-san]

Another anagram:

Spoiler for In keeping with the story

Gold stone, or gold lines or gold something...I have no idea

[Molly Mae]

Spoiler for The Last Riddle

Cones