Math Is Fun Forum

Olinguito

Member

Registered: 2014-08-12

Posts: 649

Mate in three?

This is a chess problem from The Illustrated London News, a 19th-century publication. According to the author it is possible for white to mate in three moves but I can't find a solution.

[list=*]
[*][/*]
[/list]

The best I can do is

I analysed the problem at http://www.chesslab.com/PositionSearch.html but it couldn't find a mate-in-three either; however it did find an

Can anyone find a mate in three, if there is one? Phrontister?

Last edited by Olinguito (2015-03-23 21:13:01)

---

Bassaricyon neblina

SteveB

Member

Registered: 2013-03-07

Posts: 595

Re: Mate in three?

I couldn't have solved it myself, but my chess computer can mate in 3 against any defence.
It gives the main line as:
1. Qb5  d1-Q
2. Nxb3  axb3
3. Qd5+ (checkmate)

Last edited by SteveB (2015-03-23 00:03:17)

Olinguito

Member

Registered: 2014-08-12

Posts: 649

Re: Mate in three?

Oh, I didn't see that. Thanks, SteveB.

---

Bassaricyon neblina

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Mate in three?

What if black goes Tc5 on the first move?

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Mate in three?

What is T?

---

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

SteveB

Member

Registered: 2013-03-07

Posts: 595

Re: Mate in three?

If you mean T to mean the rook takes c5 then:

1. Qb5   Rxc5
2. Qd7+ Kxe5
3. Ng4+ (checkmate)

Or if you mean the knight takes c5 then:

1. Qb5  Nxc5
2. Ng4  c1=Q
3. e3+  (checkmate)

Last edited by SteveB (2015-03-23 03:14:20)

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Mate in three?

Why wouldn't the king go to c4 in the second move in the first case?

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

SteveB

Member

Registered: 2013-03-07

Posts: 595

Re: Mate in three?

That variation results in Qxa4+

as in:
1. Qb5    Rxc5
2. Qd7+  Kc4
3. Qxa4+ (checkmate)

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Mate in three?

So, all the variations end up with a mate?

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Olinguito

Member

Registered: 2014-08-12

Posts: 649

Re: Mate in three?

This is a much more interesting puzzle than I thought. If indeed all variations end with mate in three, it must have taken a super genius brain to work them out, given there were no computers in the 19th century. I can see why it won first prize.

Last edited by Olinguito (2015-03-23 05:01:31)

---

Bassaricyon neblina

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,877

Re: Mate in three?

1. Nxb3+ Kd5
2. Nxd2+ Rc4
3. Bxc4#

In this variation Black's king is forced by two discovered checks to move to safety himself because White's checking pieces (first the queen, then the bishop) cannot be captured and Black has no blocking pieces with which to shield the king from them.

Other than the above, the Black king's only move option is on his first move: ie, Kc4...but that leads to mate-in-2 with Nxd2#.

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Mate in three?

Um, phro, I don't think the black king can go to d5.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,877

Re: Mate in three?

Oops! Thanks, stefy. I'd placed White's Nf6 on Ng6. >{blush,grumble}<

Yes, Black can't prolong the game beyond mate-in-3 with White = 1. Qb5 (as per SteveB). I tried all possible options.

Last edited by phrontister (2015-03-23 16:47:39)

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Mate in three?

So, all the variations end up with a mate?

There are also many ways to iterate the game infinitely

---

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,877

Re: Mate in three?

There are also many ways to iterate the game infinitely

Sorry, Agnishom, but I don't know what you mean by that.

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Mate in three?

1. Rh1 Rf8
2. Rh3 Rd8
3. Rh1 Rf8
4. Rh3 Rd8
.
.

---

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Mate in three?

None of those is an optimal move, so it would never happen.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,877

Re: Mate in three?

1. Rh1 Rf8
2. Rh3 Rd8
3. Rh1 Rf8
4. Rh3 Rd8
.
.

Black would be very pleased indeed if White went 5. Rh1!

There are also many ways to iterate the game infinitely

'Infinitely' is not possible these days under FIDE Laws of Chess.

Last edited by phrontister (2015-03-25 01:07:50)

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

applejuicefool

Member

Registered: 2015-09-19

Posts: 3

Re: Mate in three?

What about:

1.    Nd3+(discovered)           Kc4 (forced)
2.    Bxb3+                           a4xb3 (forced)
3.    Qb4++               

I just did this looking at the diagram, so I might have missed something...

Last edited by applejuicefool (2015-09-19 15:56:11)

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,877

Re: Mate in three?

Hi applejuicefool;

1.    Nd3+(discovered)           Kc4 (forced)

Kc4 isn't forced, as Black has an alternative with Rc5 to block White's queen. That leads to mate in four.

---

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson