POTW 2

I notice that "Problems are available at the bulletin board outside Roop 119." What is this new-fangled educational tool you have at GMU, called a Roop? They must be pretty good since you seem to have at least 119 of them.

Ahem. We are JMU. GMU refers to our rivals George Mason University.

OK JMU, what's a little spelling among friends. You are my friend aren't you?
Now, what about "Roop"?

I assume you would rather not have solutions posted online before Friday where contestants can see them, but I was able to get from
A--X to BXX
BXX.....A--X in 17 moves but it took 18 to get to

B--X
AXX

A minor difficulty with the problem sheet you posted, with respect to the form of the answer you suggested: you didn't name the other three items and their initial starting locations. (and the illustration is doesn't allow one to easily identify what those objects are). So to solve the problem we first have to assign a name and location to those other 3.

(hockey puck, mug, candle holder?)

And I was able to to the exchange in 17 moves, except it left two of the other pieces in different spots than their starting locations. I.e.,:
Started with
W-1
B23

Ended with
B12
W-3

So I solved the specific narrow problem posed (exchanging W and B), but I'm not sure whether the location of the other 3 items was supposed to be the same or not.

Divalent, I cheated and used a computer. Following your notation, it turns out it is impossible to reach the arrangement where W and B are switched and the remaining items are in their starting positions. (In fact half of the possible arrangements of items are unattainable.) There is also a second solution with 17 moves.

All that is required is that the flask and the brush be transposed. It makes no difference where the other items end up. The other three items are a mousetrap, a pepperbox and an iron. But it's certainly fine just to label them A-E and got from there.

I've been traveling and haven't had a chance to really sit down and solve this one. Like others I first read it to intend that the other items should end up in the same locations. Bu t I knew from experience with similar puzzles that, in general,z half of the posible arrangements cannot be reached, including those in which the location of two items as switched and all the others remain in the same place. So I am not suprised that this first reading was incorrect.

Rick, I made the same incorrect first reading as well and proceeded to be driven crazy from attempting to do the impossible. The following (taken from http://www.jwstelly.org/CyclopediaOfPuzzles/PuzzlePage.php?puzzleid=Pz8…) from what I assume is the original presentation of the puzzle gives a slightly stronger hint that the other items don't need to end up in the same places by referencing them without imposing the limitation:

"It is only necessary to mention that the whisky flask represents the bedstead and the scrubbing brush may be taken for the ice box, and that you are to transpose the positions of these two articles by moving one piece at a time in a sequence of plays in which the flat-iron, pepper box and mouse trap may be used to advantage."

Jason,

I enjoy your POTW series, so I already looked at and solved (don't worry, I won't post it on your blog) your POTW 3. I do think, for the sake of completeness, though, that you need to edit the statement of the problem. Since I know the rules of chess, this was not problematic for me, but you should indicate in the statement of the problem that the queen may not move to a square adjacent to the king. That's obvious to a chess player, but maybe not to a non-chess player. Without that restriction, the following is a valid solution, and I am sure that you do not want it to be one:

1. Qb1+ Kd2
2 Qc1+ Kd3

Sean T,
I've searched the rules of chess and I cannot find any prohibition on the queen moving adjacent to the king.

A little late to the conversation about lines but the comments over there are shut off. y=mx+b is not a linear function, it is called an affine function. To stay safe, call y=mx+b a linear equation.

Peter,

Okay, that's not the actual rule in chess, but for the purpose of this problem it's equivalent. The rules of chess allow the king to capture the queen if it moves to a square adjacent to the king. If this happens, obviously, the king cannot be forced to move to d3, and the problem cannot be solved. Therefore, disallowing a move by the queen to a square adjacent to the king eliminates the two-move solution I posted above.

I know it seems nit-picky since it's likely that most people reading the problem know enough about chess to know that the pieces can be captured. However, in the problem it is stated that no chess knowledge is needed to solve the problem. Whether you want to state that the queen cannot move to a square adjacent to the king or that the king is allowed to capture the queen if it can legally move to a square occupied by the queen is really not the point. The point is that there is a missing axiom in the statement of the problem. This missing axiom leads to an unintended (I am assuming) valid solution, assuming that you follow the rules as stated in the problem and not the actual rules of chess.

Greetings Jason,

My blog may be off subject but i am experiencing a very serious situation and i require you & others urgent assistance... I dont know exactly what to do....i'll explain.

I am a private practicing grassroots research scientist just over 18 yrs in the field of Socio-Economics and i am more than thrilled to inform you and others that i have made great discoveries & made sound developments in workforce development and economic upgrades that will accurately aid everyone in the areas where needed all that is required is certification of my work....

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