Solution to Sudoku no 722

Sudoku no 722 (Easy)

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Solution to Maths Problem no 2

Here is one way to work it out, which will only make sense if you can program in C:

andrew@ASUS-Laptop:~/Maths_Problems$ cat multiply.c
#include <math.h>
#include <stdio.h>
#include <stdlib.h>

void para_a (void);
void para_b (void);
void para_c (void);
void para_d (void);

/* Global variables. */

int a;
int b;
int c;
int d;

int main ()
{
para_a();
}
void para_a ()
{
for (a = 1; a <= 9; a++) para_b();
}
void para_b ()
{
for (b = 0; b <= 9; b++) para_c();
}
void para_c ()
{
for (c = 0; c <= 9; c++) para_d();
}
void para_d ()
{
for (d = 0; d <= 9; d++)
  {
  if ((a!=b)  && (a!=c) && (a!=d) && (b!=c) && (b!=d) && (c!=d))
    {
    if (9*(1000*a+100*b+10*c+d) == 1000*d+100*c+10*b+a)
      printf("%d %d %d %d\n", a, b, c, d);
    }
  }
}
andrew@ASUS-Laptop:~/Maths_Problems$ cc -o multiply multiply.c
andrew@ASUS-Laptop:~/Maths_Problems$ ./multiply
1 0 8 9
andrew@ASUS-Laptop:~/Maths_Problems$

Maths Problem no 2

Find a four digit number which you can multiply by 9 to give the same four digits in reverse order. All four digits must be different and the first digit of the original number must not be zero:

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Solution to Sudoku no 721

Sudoku no 721 (Tough)

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Solution to Maths Problem no 1

Maths Problem no 1

Puzzles like this appeared in Computer Weekly in the '80s and '90s. As they were in a computing magazine I often wrote a BASIC program to solve them. However, my son worked this one out using pencil and paper in around 15 minutes. I created it using Oracle Database Version 18 Express Edition.

Replace the letters in the addition sum below so that the answer is correct. Use each of the numbers 1 to 9 exactly once and assume that O=1, R=5 and E=2:

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Chess Solution no 22

 

1. Rc8+  Kg7

2. Bf6+  Kh7

3. Rh8+  Kg6

4. Rg8+ 1-0 (as black will lose her bishop)

Chess Puzzle no 22

The position below is from Anna Muzychuk versus Zhongyi Tan, FIDE Women's World Cup, 2023, Baku, Azerbaijan. It is white's turn to play. Try to work out how the game continued:

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Solution to Sudoku no 720

Sudoku no 720 (Extreme)

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Chess Solution no 21

The game continued as follows: 

1 …  Rg1+

2 Bd1  Rxc2+

3 Kb1  Rxd1+

4 Nxd1  Rc5+

5 Ka1  Rc1# 

Here is a slightly different solution:

1 …  Rxc2+

2 Kb1  Rg1+

3 Bd1  Rxd1+

4 Nxd1  Rc5+

5 Ka1  Rc1#

Chess Puzzle no 21

This position is from Tore Colas versus James C Mansson, Hastings 2005. Black to play and checkmate in five moves. There are two possible solutions:

 

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Solution to Sudoku no 719

Sudoku no 719 (Tough)

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Chess Solution no 20

1. ...  Rb2

2. g4  Na5

3. Rxa5  bxa5

winning the exchange.

Note that if:

4. Nxa5

then:

4. ...  Kb6

or:

4. ...  Rb5

and white's knight is lost.

Chess Puzzle no 20

The position below is from Walter Burnett versus Mark Broom, Glasgow, 2003. It is black's move. What should he play?

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Solution to Sudoku no 718

Sudoku no 718 (Easy)

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Chess Solution no 19

1. Bb6!

Black then resigned.

If he had not, the game might have continued as follows:

1. ...  Qxb6

2. Nxe7+  Kh8

3. Nxc8  Qb7

4. Nxd6  Nxd6

5. exd6

or:

1. ...  exf5

2. Bxc7  Rxc7

or:

1. ...  Qd7

2. Nxe7+  Qxe7

3. Bxa5

Chess Puzzle no 19

The position below is from Feliks J Kwiatkowski (a member of Haywards Heath chess club) versus Jerry Humphreys, Birmingham, 2005. It is white's turn to play. What is his best move?

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Chess Solution no 18

 

Analysis suggests the following solution: 

 

1. ...  Qxf2+

2. Kh1  Qf3+

3. Kg1 (or Kh2)  Qxg3+

4. Kh1  Qh2#

 

However, the game continued like this:

 

1. ...  Qxf2+

2. Kh1  Qe1+

 

... and white resigned. It is not clear whether he thought he was going to lose his bishop by:

 

3. Kh2  Qxc1

 

... or whether he spotted two further solutions to my original problem:

 

1. ...  Qxf2+

2. Kh1  Qe1+

3. Kh2  Qxg3+

4. Kh1  Qh2#

... and:

1. ...  Qxf2+

2. Kh1  Qe1+

3. Qf1  Qxf1+

4. Kh2  Rf2#

Chess Puzzle no 18

This position is from Pierre Fox versus James C Mansson, Hastings, 2006. Black to play and checkmate in 4 moves:

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Solution to Sudoku no 717

Sudoku no 717 (Diabolical)

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Chess Solution no 17

1. b8=N+ 

Black then resigned.

You get no marks for the following answer:

1. b8=Q  Nc6+

2. Kd5  Nxb8

Chess Puzzle no 17

This position is from Ilya Smirin versus Tal Baron, Acre, 2013. It is white to play. What should he do?

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Solution to Sudoku no 716

Sudoku no 716 (Easy)

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Chess Solution no 16

 

1. Qe8+  Kg7

2. Nf5+  Kf6

3. Qe6#

Chess Puzzle no 16

This position is from jaeger1 versus seanhoran. It was played on Gameknot in 2019. White to play and checkmate in 3 moves:

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Solution to Sudoku no 715

Sudoku no 715 (Diabolical)

Our younger son created this sudoku using a Javascript program which he wrote himself:

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Chess Solution no 15

The game continued as follows:

1. Nxf6+  Qxf6

2. Qxh7+  Kf8

3. Ne4  Qxb2

4. Nxd2

At this point, Tal resigned.

Notice that if:

4. ...  Qxd2

5. Rxc8+  Rxc8

6. Qh8+  Ke7

7. Qxc8

Chess Puzzle no 15

The position below is from Oleg M Romanishin versus Mikhail Tal, Barcelona, 1992. It is white to play. Try to work out how the game continued:

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Solution to Sudoku no 714

Sudoku no 714 (Extreme)

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Chess Solution no 14

1. ...  Rxh5+

2. Kg4  Rg5+

3. Kf4  Qxg3+

4. Ke4  Re5+

5. Kd4  Qe3#

 

or

 

1. ...  Rxh5+

2. Kxh5  Qg6+

3. Kh4  Qg5+

4. Kh3  Qh5#

 

etc.

Chess Puzzle no 14

This position is from a game apparently played by Capablanca. According to the web site where I found it, the other player was born 50 years after Capablanca died so I will not be giving his name as it is clearly incorrect. Black to play and checkmate in 5 moves:

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Solution to Sudoku no 713

Sudoku no 713 (Easy)

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Solution to Sudoku no 712

Sudoku no 712 (Diabolical)

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Solution to Sudoku no 711

Sudoku no 711 (Diabolical)

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Solution to Sudoku no 710

Sudoku no 710 (Tough)

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Chess Solution no 13

The game continued as follows:

47. ...  Rxd5+

48. Ke2  Qc2+

49. Ke3  Rd3+

50. Ke4  Rd4+

White resigned at this point. There are alternative scenarios but they all involve the loss of the white queen in exchange for the black rook e.g:

47. ...  Rxd5+

48. Ke2  Qc2+

49. Kf3  Rf5

 

etc.

Chess Puzzle no 13

You may remember Sarasadat Khademalsharieh (AKA Sara Khadem) as the Iranian chess player who removed her hijab while competing in a tournament in Kazakhstan. Realising that she would be arrested if she returned to Iran, she defected to Spain instead and now has Spanish nationality.

The position below is from the game she played in that tournament against Nafisa Muminova. Sarasadat has the black pieces and it is her turn to move. How did she bring the game to a successful conclusion?

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