Odd eBay Chess Listing

People's ingenuity never ceases to amaze me:

http://cgi.ebay.com/CHESS-PROBLEM-SOLVE-500-REWARD-/190484908966?pt=US_Nonfiction_Book&hash=item2c59c90ba6

Great!

I wonder what it'll sell for 🙂

toet.

Originally posted by toeternitoe
Great!

I wonder what it'll sell for 🙂

toet.

Well. it's a "Buy it now". You're basically placing a $5 bet, with a 100-to-1 payoff, that you'll be the first one to solve the problem. The catch is that you have to pay to see the problem, and there's no guarantee that there's even a solution. It's not a bet that I'd make.

Originally posted by Mad Rook
Well. it's a "Buy it now". You're basically placing a $5 bet, with a 100-to-1 payoff, that you'll be the first one to solve the problem. The catch is that you have to pay to see the problem, and there's no guarantee that there's even a solution. It's not a bet that I'd make.

Didn't know that 😳
I've never shopped on ebay

That's quite a gamble indeed.But low stakes 😉

toet.

Originally posted by Mad Rook
People's ingenuity never ceases to amaze me:

http://cgi.ebay.com/CHESS-PROBLEM-SOLVE-500-REWARD-/190484908966?pt=US_Nonfiction_Book&hash=item2c59c90ba6

Blurb from listing

I have never solved it without having two Bishops of the same color on the same color squares – NOT a true solution because Chess Rules won’t allow it.

Originally posted by adramforall
Blurb from listing

I have never solved it without having two Bishops of the same color on the same color squares – NOT a true solution because Chess Rules won’t allow it.

Really? What if you had both your Bishops remaining, and promoted a pawn to a Bishop? Is that a possibility?

Sounds like a complete p''''' take to me. $5 to solve a problem that they won't tell you until you pay and there are no refunds. I've just sent him a message and I won't tell you waht it said. Tsk tsk

Edit: I just tried to ask him a question. I was going to ask 'are you a ***t'. I wasn't even granted this request. I was told

"We're sorry we couldn't find an answer for you. Unfortunately, this seller is not able to respond to your question. We suggest reviewing the item again to see if your answer is in the seller's listing."

SHARK!!!!!!!!!!!

Thought SG may have got this (perhaps not seen it yet).

This clue:

"I have never solved it without having two Bishops of the same color
on the same color squares – NOT a true solution because Chess Rules
won’t allow it."

The lad must be referring to a famous unsolved puzzle where you have to
cover every square on a chessboard with the pieces only.
(I don't think it has been solved).

This comes close.


But you always have one square left (here e2).

Is chess that perfect that it cannot be done and there must always be
a square left for the Black King.

Well it can be done thus:


But illegal as there are two white squared Bishops.

This must be the problem the lad is setting.

Edit:

He says he invented this problem 40 years ago.....1970? I bet SG can
find an older example of this being set. The above two postions came
from a book published in 1963 saying it cannot be done.

The Complete Book of Chess by Horowitz & Rothenburg.

His Blurb:

"I “conjured” up this problem about 40 years ago and call it “Mickey’s Eclipse”
(after guess who – ME).

I have never solved it without having two Bishops of the same color on the
same color squares – NOT a true solution because Chess Rules won’t allow it.
The best that I’ve been able to do otherwise is come to within 1 square of a
solution. If you can be the 1st to solve this, and message me (thru Ebay)
before anyone else does, – you will be entitled to the reward of $500."

Originally posted by greenpawn34
Thought SG may have got this (perhaps not seen it yet).

This clue:

"I have never solved it without having two Bishops of the same color
on the same color squares – NOT a true solution because Chess Rules
won’t allow it."

The lad must be referring to a famous unsolved puzzle where you have to
cover every square on a chessboard with the pieces only.
(I don't think it has been solved).

Nice work, Detective Greenpawn! I get to play without paying! 😏

I agree that it sure looks like he's referring to this problem. It would make sense - There's almost no chance of him having to pay out. Thanks!

It's a little odd that he says he "conjured up" this problem. Poetic license? Poor memory? Or did he take the original problem and turn the board around to make it different? 😉 Or maybe he used black pieces instead of white pieces?

On a side note, I wonder if any of the problemist guys have tried writing a program to solve this problem. Either find solution(s) or prove that none exist.

I think that the number of possible positions would be:

32 x 32 x 62 x 61 x 60 x 59 x 58 x 57 = 4.53 x 10^13 (45.3 trillion)

If someone wrote a program to evaluate each position for all squares being covered, and assuming that the program could evaluate 200,000 positions/sec (a total swag), then it would take about 7.2 years to solve.

There must be someone out there crazy enough to do this. 🙄

Originally posted by Mad Rook
32 x 32 x 62 x 61 x 60 x 59 x 58 x 57 = 4.53 x 10^13 (45.3 trillion)

Due to symmetry, you could regard the king as only having 10 unique squares. Also, if there's e.g. 58 empty squares left to place the knights, then that's (58 * 59)/2 unique possbilities rather than 58 * 57. Likewise for the placement of the rooks. That drops your time to around 100 days. I'm sure other symmetry, heuristics, etc. will get this down further more. I think it's doable and has probably been done. 🙂

I'd say eyeballing the puzzle, it looks like there is no solution. Coming from a math background, one thing I'm midly curious about with these kinds of puzzles, is can we mathematically prove there is no solution without bruteforcing every possibility?

For example, maybe it could be proven there is no solution by deriving a contradiction. Let's suppose a solution exists, what properties must that solution have and can we show that the pieces on the board cannot satisfy those properties?

My first attempt would be this: There are 64 squares on the board that must be covered. How many squares total do all the pieces cover? What's the least amount of overlap possible? (This would be the tricky part) Is the total coverd squares possible minus overlap at least 64?

You should assign this as homework to a college freshman math course, and then steal their work and publish the answer as your own.

Originally posted by SmittyTime
You should assign this as homework to a college freshman math course, and then steal their work and publish the answer as your own.

Haha, I was hoping someone here in the forums would do it for me!