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Sequence

jfgw
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Sequence

#133516

Postby jfgw » April 20th, 2018, 1:41 pm

What comes next in this sequence, and why?
Image
Image: Julian F. G. W.

(If you don't want to draw it, a description will suffice.)

Julian F. G. W.

malkymoo
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Re: Sequence

#134505

Postby malkymoo » April 24th, 2018, 5:38 pm

Well, I've been racking my brains over this, but can't see the solution. Would you like to post a clue?

jfgw
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Re: Sequence

#134508

Postby jfgw » April 24th, 2018, 5:52 pm

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.

jfgw
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Re: Sequence

#134768

Postby jfgw » April 25th, 2018, 7:51 pm

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.

UncleEbenezer
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Re: Sequence

#134796

Postby UncleEbenezer » April 25th, 2018, 9:57 pm

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?)

jfgw
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Re: Sequence

#134809

Postby jfgw » April 25th, 2018, 11:08 pm

UncleEbenezer wrote:(Erm, are we waving flags here?)

Nothing to do with flags.

Gengulphus
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Re: Sequence

#134846

Postby Gengulphus » April 26th, 2018, 8:49 am

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

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Re: Sequence

#134848

Postby Gengulphus » April 26th, 2018, 9:19 am

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

jfgw
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Re: Sequence

#134959

Postby jfgw » April 26th, 2018, 5:03 pm

Well done Gengulphus, that is the correct answer.

Julian F. G. W.

cinelli
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Re: Sequence

#135727

Postby cinelli » April 30th, 2018, 11:39 am

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

jfgw
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Re: Sequence

#135763

Postby jfgw » April 30th, 2018, 1:42 pm

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.

GoSeigen
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Chess

#135779

Postby GoSeigen » April 30th, 2018, 2:31 pm

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


jfgw
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Re: Sequence

#135782

Postby jfgw » April 30th, 2018, 2:43 pm

GoSeigen wrote:Queens can't jump over pawns!


Oops, I missed the pawn off :(

Julian F. G. W.

jfgw
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Re: Sequence

#135788

Postby jfgw » April 30th, 2018, 3:02 pm

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.

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Re: Chess

#135789

Postby UncleEbenezer » April 30th, 2018, 3:03 pm

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.

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Re: Sequence

#135797

Postby GoSeigen » April 30th, 2018, 3:39 pm

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

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Re: Chess

#135801

Postby GoSeigen » April 30th, 2018, 3:56 pm

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


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Re: Sequence

#135866

Postby jfgw » April 30th, 2018, 8:44 pm

You can set the pieces up here,

https://lichess.org/editor

then 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.

cinelli
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Re: Sequence

#136451

Postby cinelli » May 2nd, 2018, 9:16 pm

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

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Re: Sequence

#136474

Postby GoSeigen » May 3rd, 2018, 2:15 am

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


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