Page 1 of 2
Sequence
Posted: April 20th, 2018, 1:41 pm
by jfgw
What comes next in this sequence, and why?
Image: Julian F. G. W.(If you don't want to draw it, a description will suffice.)
Julian F. G. W.
Re: Sequence
Posted: April 24th, 2018, 5:38 pm
by malkymoo
Well, I've been racking my brains over this, but can't see the solution. Would you like to post a clue?
Re: Sequence
Posted: April 24th, 2018, 5:52 pm
by jfgw
malkymoo wrote:Well, I've been racking my brains over this, but can't see the solution. Would you like to post a clue?
A sequence can exist for many different reasons, for example:
A, C, E, G, I, K... are the odd-numbered letters;
A, E, F, H, I, K... are the capital letters made up only of straight lines;
J, F, M, A, M, J... are the first letters of the months.
You need additional knowledge (you need to know the names of the months) to understand the third example.
Julian F. G. W.
Re: Sequence
Posted: April 25th, 2018, 7:51 pm
by jfgw
jfgw wrote:You need additional knowledge (you need to know the names of the months) to understand the third example.
You need additional knowledge to deduce the answer to this puzzle. I would expect everyone on this board to have that knowledge.
Julian F. G. W.
Re: Sequence
Posted: April 25th, 2018, 9:57 pm
by UncleEbenezer
jfgw wrote:jfgw wrote:You need additional knowledge (you need to know the names of the months) to understand the third example.
You need additional knowledge to deduce the answer to this puzzle. I would expect everyone on this board to have that knowledge.
Julian F. G. W.
Phew! Thank Julian for that!
(Erm, are we waving flags here?)
Re: Sequence
Posted: April 25th, 2018, 11:08 pm
by jfgw
UncleEbenezer wrote:(Erm, are we waving flags here?)
Nothing to do with flags.
Re: Sequence
Posted: April 26th, 2018, 8:49 am
by Gengulphus
I think the 6th diagram in the sequence is an X just like the 3rd; if so, I know what the 7th and 8th are as well, and I don't believe it has a 9th or later diagram.
It is closely related to a number sequence that starts 18, 14, 2, 17, 11, 2 and has only two more numbers after that.
Gengulphus
Re: Sequence
Posted: April 26th, 2018, 9:19 am
by Gengulphus
Since posting the above, I've noticed the "and why?" part of the OP, so here's my reason - treated as a spoiler:
They are diagrammatic representations of the movement capabilities of the pieces on the back row of the starting position in a game of chess, viewed from the white side of the board. And my number sequence is just the standard one-letter abbreviations of the same pieces (R, N, B, Q, K, B, N, R) converted to their positions in the alphabet.
Gengulphus
Re: Sequence
Posted: April 26th, 2018, 5:03 pm
by jfgw
Well done Gengulphus, that is the correct answer.
Julian F. G. W.
Re: Sequence
Posted: April 30th, 2018, 11:39 am
by cinelli
Time for a chess puzzle, I think. I seem to remember that the old Fool had a chess board but that it was not very active. White pieces are upper case and black lower case and italics and bold. I will give credit to the setter with the solution.
. --- --- --- --- --- --- --- ---
8 | b | | | | | | | |
--- --- --- --- --- --- --- ---
7 | | | | | | | | |
--- --- --- --- --- --- --- ---
6 | | | | | | | | |
--- --- --- --- --- --- --- ---
5 | | | | Q | B | | | |
--- --- --- --- --- --- --- ---
4 | | | | | | | | |
--- --- --- --- --- --- --- ---
3 | | | | | | K | | N |
--- --- --- --- --- --- --- ---
2 | P | | | | | | | |
--- --- --- --- --- --- --- ---
1 | | | | | | | | k |
--- --- --- --- --- --- --- ---
a b c d e f g h
White to mate in three moves against any defence. At first glance this looks simple because black has no moves. But 1 Qxa8? is a stalemate draw while 1 Bd4 Bxd5+ 2 Kg3 Bxa2 3 Nf2+ is not mate because of Kg1.
Cinelli
Re: Sequence
Posted: April 30th, 2018, 1:42 pm
by jfgw
Spoiler
. --- --- --- --- --- --- --- ---
8 | b | | | | | | | |
--- --- --- --- --- --- --- ---
7 | | | | | | | | |
--- --- --- --- --- --- --- ---
6 | | | | | | | | |
--- --- --- --- --- --- --- ---
5 | | | | Q | B | | | |
--- --- --- --- --- --- --- ---
4 | | | | | | | | |
--- --- --- --- --- --- --- ---
3 | | | | | | K | | N |
--- --- --- --- --- --- --- ---
2 | P | | | | | | | |
--- --- --- --- --- --- --- ---
1 | | | | | | | | k |
--- --- --- --- --- --- --- ---
a b c d e f g h
White's knight to F2 puts black into check. Black's only move is king to G1.
. --- --- --- --- --- --- --- ---
8 | b | | | | | | | |
--- --- --- --- --- --- --- ---
7 | | | | | | | | |
--- --- --- --- --- --- --- ---
6 | | | | | | | | |
--- --- --- --- --- --- --- ---
5 | | | | Q | B | | | |
--- --- --- --- --- --- --- ---
4 | | | | | | | | |
--- --- --- --- --- --- --- ---
3 | | | | | | K | | |
--- --- --- --- --- --- --- ---
2 | P | | | | | N | | |
--- --- --- --- --- --- --- ---
1 | | | | | | | k | |
--- --- --- --- --- --- --- ---
a b c d e f g h
White can now take black's bishop with his queen. Black's only move is king to F1.
. --- --- --- --- --- --- --- ---
8 | Q | | | | | | | |
--- --- --- --- --- --- --- ---
7 | | | | | | | | |
--- --- --- --- --- --- --- ---
6 | | | | | | | | |
--- --- --- --- --- --- --- ---
5 | | | | | B | | | |
--- --- --- --- --- --- --- ---
4 | | | | | | | | |
--- --- --- --- --- --- --- ---
3 | | | | | | K | | |
--- --- --- --- --- --- --- ---
2 | P | | | | | N | | |
--- --- --- --- --- --- --- ---
1 | | | | | | k | | |
--- --- --- --- --- --- --- ---
a b c d e f g h
White moves his queen to A1 for check mate.
. --- --- --- --- --- --- --- ---
8 | | | | | | | | |
--- --- --- --- --- --- --- ---
7 | | | | | | | | |
--- --- --- --- --- --- --- ---
6 | | | | | | | | |
--- --- --- --- --- --- --- ---
5 | | | | | B | | | |
--- --- --- --- --- --- --- ---
4 | | | | | | | | |
--- --- --- --- --- --- --- ---
3 | | | | | | K | | |
--- --- --- --- --- --- --- ---
2 | P | | | | | N | | |
--- --- --- --- --- --- --- ---
1 | Q | | | | | k | | |
--- --- --- --- --- --- --- ---
a b c d e f g h
Julian F. G. W.
Chess
Posted: April 30th, 2018, 2:31 pm
by GoSeigen
jfgw wrote:Spoiler
White moves his queen to A1 for check mate.
Julian F. G. W.
Queens can't jump over pawns!
Spoiler:
1. Kg3 bxQ
2. Bd4 b moves anywhere
3. Nf2 mate
if ...
1. ... kg1
2. Qd1 mate
Re: Sequence
Posted: April 30th, 2018, 2:43 pm
by jfgw
GoSeigen wrote:Queens can't jump over pawns!
Oops, I missed the pawn off
Julian F. G. W.
Re: Sequence
Posted: April 30th, 2018, 3:02 pm
by jfgw
GoSeigen wrote:1. Kg3 bxQ
2. Bd4 b moves anywhere
3. Nf2 mate
It wouldn't be mate as the knight is blocking the white bishop. Black could move his king to g1.
Julian F. G. W.
Re: Chess
Posted: April 30th, 2018, 3:03 pm
by UncleEbenezer
GoSeigen wrote:Spoiler:
1. Kg3 bxQ
2. Bd4 b moves anywhere
3. Nf2 mate
if ...
1. ... kg1
2. Qd1 mate
Yours is broken, too (it was my immediate "solution", but seemed too easy until I double-checked). Move 3 opens g1 to the king.
And your "if" is an illegal move: the knight at h3 prevents K-g1.
There's a similar fallacy K-f2-f1 followed by N-f2, but that fails because the black bishop can point at f1.
Re: Sequence
Posted: April 30th, 2018, 3:39 pm
by GoSeigen
jfgw wrote:GoSeigen wrote:1. Kg3 bxQ
2. Bd4 b moves anywhere
3. Nf2 mate
It wouldn't be mate as the knight is blocking the white bishop. Black could move his king to g1.
Julian F. G. W.
Oops, quite right. That'll teach me to try it on an ASCII chess board!
GS
Re: Chess
Posted: April 30th, 2018, 3:56 pm
by GoSeigen
GoSeigen wrote:Okay, how about:
1. Br2 kxB
2. Qxb kxN
3. Qh8 mate
if ...
2. ... kh1
3. Kg3 mate
or
1. ... bxQ+
2. Kg3 bishop moves anywhere
3. Nf2 mate
Also using ASCII board so may be wrong!
GS
Re: Sequence
Posted: April 30th, 2018, 8:44 pm
by jfgw
You can set the pieces up here,
https://lichess.org/editorthen click "Analysis Board" and try out some moves.
Here's the starting position for the present puzzle,
https://lichess.org/editor/b7/8/8/3QB3/ ... k_w_KQkq_-Julian F. G. W.
Re: Sequence
Posted: May 2nd, 2018, 9:16 pm
by cinelli
Firstly apologies for not starting this as a new thread.
GoSeigen has it: Bh2 is the key move. This chess puzzle was set by Peter Orlik who, Wikipedia tells me, is an American mathematician who specialises in topology, algebra and combinatorics. At least I suppose it the same chap. Chess correspondent Leonard Barden reported on the problem and admitted that it took him 20 minutes to find the key move.
Cinelli
Re: Sequence
Posted: May 3rd, 2018, 2:15 am
by GoSeigen
cinelli wrote:Firstly apologies for not starting this as a new thread.
GoSeigen has it: Bh2 is the key move. This chess puzzle was set by Peter Orlik who, Wikipedia tells me, is an American mathematician who specialises in topology, algebra and combinatorics. At least I suppose it the same chap. Chess correspondent Leonard Barden reported on the problem and admitted that it took him 20 minutes to find the key move.
Cinelli
It was an interesting puzzle as it had a number of elements: pinned queen, discovered check, stalemate, sacrifice of multiple pieces and a bishop-knight checkmate. I think Barden must have made a meal of it though, it was simplified if you:
-focused on how the mate had to be achieved
-realised the w. queen was practically useless
-kept pieces off squares accessible to black bishop
GS