Chess Problem
Consider a 5×5 chess board. Is it possible to place five queens on the board such that three pawns can safely be placed on the board? In other words, by carefully choosing where to place the five queens, can you arrange it so that there are three squares on the board that none of the queens can attack?
nope, can put 5 queens with 3 pawns safe. email me at [email protected] for a hint
you can only put 4 queens down for the three pawns to be safe, so no.
Email me at [email protected] — I don’t want to post the soln
no, that will kill every square.
place the five queens vertically at the side of the board… thats all!!1
place the 5 queens on the side vertically…. alll
Sadly very busy and cannot update more than once a month or so; hope there is enough there for you to enjoy for awhile.
What’s up to every , for the reason that I am actually keen of reading this blog’s post to be updated
daily. It contains pleasant data.
almost…HaHa!) Great job. I really enjoyed what you had to say
sent hint (sjm1 AT williams.edu)
after days of trying i realized that i need the soln. can you mail it.
there is a way — will send a hint first.
there is no answer for this riddle. maximum safe point for this riddle is 2. if this is wrong can you email me the correct answer.
thanks
ok, hint/answer sent (sjm1 AT williams.edu)
We tried a lot and we didnt find the answer.
sure, one of my favorites — sent (sjm1 AT williams.edu)
I also would like to know the calculations/algorithms behind such a problem. I could only figure it out through logical trial and error, as well.
there’s ways to cut down on the trial and error //s
Steve,
Could you email me the solution? This one has been bothering me for a while. Also, is there any method to go about finding the solution besides simple trial and error?
thanks
you didn’t include your email — email me at sjm1 AT williams.edu
hi sir steve! Its almost two weeks i am trying to solve this problem. Usually i hate to give up but this time i lost. I am unable to find the answer. If u dont mind will u pls send the answer to my email.
sure. //s
Steve,
Please send me the answer. can only get two pawns or 4 queens!!!
Shane
it’s a 5×5 chessboard. you can’t place anything in F, G, or H as they don’t exist.
My solution can’t possibly be right because I found a way to place 6 pawns safely within seconds of reading the problem. My instinct tells me that the problem can’t possibly be that easy, or that I must have read it wrong, but for the life of me I can’t figure out what’s wrong with my solution.
Queens: A1, B2, C3, D4, E5
Pawns: F7, F8, G6, G8, H6, H7
The problem is there are so many possibilities, if you don’t have a good way to explore all you could miss one. I’ll email you. //s
I have no idea how to solve this problem using math (or otherwise) please E-mail math solution. From a chess perspective I’ve been placing pieces one at a time to try to cover the same area with different pieces. ex. Q (A-1) and Q (A-2) both cover (A-3,4,5) and (B-1,2) but that alone isn’t math no matter how much I will it so.
well done! enjoy the test! I’ll send comments on my soln. //s
ok
send it as a board, with places for Q and P marked. For example:
Q – – – –
Q Q – – –
Q Q – – –
– – – – P
– – – – –
I WAS NOT ABLE TO CONCENTRATE ON MY PHYSICS TEST UNTIL I SEND THE ANSWER. SO I DECIDED TO SEND THE ANSWER AND GO BACK TO STUDY.
BYE…
SEE YOUR PROBLEMS AFTER 2 WEEKS
i have the solution for this question but i dont know how to send it.
Now i will be missing for next two weeks as my exam is starting from tomorrow. But i promise that i can solve your all problems and i will do it when i will return.
sure — drop me an email at sjm1 AT williams.edu
Hi Steven Miller, I have figured it out. I would like to know the mathematical proof of this problem.
Andrew: correct: email me at [email protected] if you want my comments on the soln. //s
sure, sending //s
almost a week i am trying to solve it. it was a hard one. i gave up i want to know the solution pleeeese.
It’s a hard riddle, but the solution is connected with some of the most important and applicable math there is. Email me at [email protected] if you want a hint.
oh, your other puzzle is hard, you know
That’s true (like tic-tac-toe), but there’s something even BETTER than symmetry which reduces the number of trials even further! Email me at [email protected] if you want to chat more.
Great riddle! Keeping symmetry in mind really lets you reduce the number of trials you need.
glad you’re enjoying it — it’s related to some of the most important applied math in use!
ahahaha, this puzzle is soooooooooo good!
check again — that won’t leave 3 squares safe; it will leave at most 2.
put 4 queens in the top left corner. one queen bottom left corner. you have exactly 3 space that are untouchable.
haha, cute.
If the Queens are all white and the pawns are too, then your all set.
sure, I’ll email. this is one of my favorite problems. you need to do some brute force computations, but if you’re clever you can cut down a lot. this leads to a lot of great math. I’ll eventually write a lot about this for the teacher’s corner (which I hope to do this spring).
After struggling for a couple days with this problem, I figured it out, but only through logical trial and error. I’d love to know a combinatorical/algorithmic/logical solution to this problem. Also, I really enjoy many of your other riddles as well.
I do not believe that works. Try putting the 5 queens on a board as you say — I believe you’ll find that you cannot place 3 pawns
Bunch the queens up on the black spaces around the main white diagonal or vice versa as close to on corner as possible. The pawns go on the diagonal as close to the opposite corner as possible.
If you fill up an entire row or column then all squares are killed and you cannot place any pawns safely
Put queens in A1, A2, A3, A4, A5, which leaves B7, B8 and C8 open for the pawns
I don’t think this leads to 3 pawns safely positioned — it isn’t my soln and I thought the soln was unique — can you double check?
A1.A2. B1,B2,D1
in other words 1st Column 2 spaces are queens, same for Column 2 then Column 4 1st space is a queen.
no — this only leaves two squares open — E2 isn’t open
Easy. Again. Put the queens in an X on the bottom left of the chess board (A1 A3 B2 C1 C3) This will leave a D5, E4, E2 open for the pawns.
mukuro: nice job, glad you enjoyed it
this covers all spaces — it doesn’t leave 3 spaces free for pawns.
first row: 2
2nd row: 4
3rd: 1
4th: 3
5th: 5
right? and i have no idea how to do this by math, i just play chess sometimes and the solution just jumped into my head when i read the riddle.
Sure. This is a great example of duality — solve a related problem. Try instead to place 3 queens so that 5 pawns are safe, and then flip the pawns and queens!
I would love some logic as to how to solve this problem other than guess and check. I have solved the riddle, but am unsatisfied not knowing the logic used.
OK. I can give a hint that doesn’t give away too much, just some advice on how to help with the trial and error. The idea behind the hint is one of THE most important observations in mathematics!
Okay, I can only get it so there are 2 open spaces. I put queens in all 4 corners and then you can put the remaining queen in the middle of any side. I took combinatorics in college (math ed BA and MA) but I would have to pull out my book to use anything other than trial and error and logic which is what I’m relying on right now and not getting very far. I don’t know if I want a hint yet. I just wanted to leave a comment I guess.
Not following — please send more details to me at sjm1 AT williams.edu
a1 a2 a3 a4 a5 = queens
Not sure what you mean — can you email me a board with the pieces placed?
A1,2,3,4,5?
Are the solutions distinct or are they just rotated / reflected versions of each other? There are 9 possible first moves in tic-tac-toe, but really there are only 3 by symmetry.
if you number them A-E and 1-5 C1,D1,A2,D2,A3 an interesting question would be how many posible solutions are there. from my solution there are at least 8 i believe.
I’ll send you the answer. This is one of my favorite problems in terms of applications.
I rly want to know the answer 🙂