or
The position below is from Richard James Cannon versus Michael J Basman, Sutton, 1997. Black to play and checkmate in 5 moves.
Our younger son created this puzzle using a Javascript program which he wrote himself:
White played 1. Nd4.
The black knight was pinned against the black queen, attacked 3 times and protected twice so could be lost. At this point the game was declared as 1-0 so I assume that black resigned.
It could have continued as follows:
This would leave the position as follows, which is hopeless for black:
The position below is from Michael Adams (2735) versus Elisabeth Paehtz (2451), which took place in 2007. It is white's move. What did he play?
1. f3 captures the black rook on the next move.
If
This position is from Timo Paakkonen (2283) versus Tuomo Halmeenmaki (2154), which was played in 2012. White to move. What should he play?
13th August 2024:
I wrote my sudoku creation program back in 2012.
Then in 2022 I decided to publish a book of tough puzzles. I used my program to create puzzles again and again and passed each one to HoDoKu. I stored puzzles with a HoDoKu grade between Hard (1000) and Hard (1999) and discarded the rest. After I had created around 8000 puzzles I had the 400 tough / hard puzzles I needed for my book.
You can buy my book using the advert on this page.
Alternatively, for a chance to win a copy, solve the sudoku below. It has a HoDoKu grade of Hard (1490) so it is typical of the puzzles in my book. Send your answer to me at international_dba@yahoo.co.uk. Do not send me your address at this point. The closing date for entries is 31st October 2024. On 1st November 2024 I will choose one winner at random from all the correct solutions received and ask where to send the book.
The name of the winner and the solution will be published shortly afterwards.
1st November 2024:
This competition is now closed.
3rd November 2024:
The winner is Freddy Vargas from Colombia.
They have been reporting on the TV this morning about a worldwide Microsoft IT outage which is causing disruption at airports, railways, banks etc so I decided to see if I was affected. I switched on my Linux laptop and created the puzzle below. I connected to the Internet and graded it at SudokuWiki then I published it on Google's Blogger platform. Facebook, Twitter and Linkedin are up so I should be able to share it too:
Our younger son created this puzzle using a Javascript program which he wrote himself:
To solve this problem, I looked up pi to several decimal places then worked it out by trial and error with the PL/SQL code below:
SQL> @pi
SQL> set serveroutput on
SQL> declare
2 top number;
3 bottom number;
4 pi constant number := 3.141592654;
5 ratio number;
6 difference number;
7 save_difference number := 1;
8 save_top number;
9 save_bottom number;
10 save_ratio number;
11 begin
12 for top in 1..999 loop
13 for bottom in 1..999 loop
14 ratio := top/bottom;
15 difference := abs(pi-ratio);
16 if difference < save_difference then
17 save_difference := difference;
18 save_top := top;
19 save_bottom := bottom;
20 save_ratio := ratio;
21 end if;
22 end loop;
23 end loop;
24 dbms_output.put_line('Top: '||save_top);
25 dbms_output.put_line('Bottom: '||save_bottom);
26 dbms_output.put_line('Ratio: '||save_ratio);
27 end;
28 /
Top: 355
Bottom: 113
Ratio: 3.14159292035398230088495575221238938053
PL/SQL procedure successfully completed.
SQL>
So there you have it. The best fractional approximation to pi with a 3 digit numerator and denominator is 355/113, which is accurate to 6 decimal places i.e. 3.141593.
3.14 and 22/7 are both approximations for pi (or π).
22/7 is a fraction with a 2 digit numerator and a 1 digit denominator.
Find the best fractional approximation for pi with a 3 digit numerator and denominator.
The answer is 548834.
I used the program below to work it out:
andrew@ASUS-Laptop:~/Maths_Problems$ cat problem4e.c
#include <math.h>
#include <stdio.h>
int main()
{
double a;
double b;
double c;
double d;
double e;
double f;
int abcdef;
for(a=1;a<=9;a++)
{
for(b=0;b<=9;b++)
{
for(c=0;c<=9;c++)
{
for(d=0;d<=9;d++)
{
for(e=0;e<=9;e++)
{
for(f=0;f<=9;f++)
{
abcdef=100000*a+10000*b+1000*c+100*d+10*e+f;
if (abcdef==pow(a,6)+pow(b,6)+pow(c,6)+pow(d,6)+pow(e,6)+pow(f,6))
printf("%d\n",abcdef);
}
}
}
}
}
}
return 0;
}
andrew@ASUS-Laptop:~/Maths_Problems$
I ran it as follows:
andrew@ASUS-Laptop:~/Maths_Problems$ ./problem4e
548834
andrew@ASUS-Laptop:~/Maths_Problems$
...then I checked the result:
andrew@ASUS-Laptop:~/Maths_Problems$ echo "5^6+4^6+8^6+8^6+3^6+4^6"|bc
548834
andrew@ASUS-Laptop:~/Maths_Problems$
Find a six digit positive integer abcdef where:
abcdef = a^6 + b^6 + c^6 + d^6 + e^6 + f^6.
I worked this out using the program below. The solution is at the bottom of the page:
andrew@ASUS-Laptop:~/Maths_Problems$ cat problem1.c
#include <math.h>
#include <stdio.h>
int main ()
{
int abc;
int def;
double abcdef;
double square_root;
int solution;
for(abc=100; abc<=998; abc++)
{
def=abc+1;
abcdef=(1000*abc)+def;
square_root=trunc(pow(abcdef,0.5));
if(pow(square_root, 2)==abcdef)
{
solution=abcdef;
printf("%d\n",solution);
}
}
return 0;
}
andrew@ASUS-Laptop:~/Maths_Problems$ ./problem1
183184
328329
528529
715716
andrew@ASUS-Laptop:~/Maths_Problems$
Find all 6 digit integers ABCDEF such that:
(1) ABCDEF is a perfect square.
(2) DEF = ABC + 1.
This position is from Nick Maatman versus Luuk Baselmans, Dutch League, 2022-23. Black to play and checkmate in 6 moves:
Here is a string which you can copy to work on this puzzle online:
030006000000020800050000100000000007040608001700510690620090000900000050803000070
The game continued as follows:
Black resigned at this point.
If he had not done so, the game might have continued as follows:
However, whatever he did, black was going to lose his queen. His best (or least worst) option seems to be:
The position below is from Alekhine versus Isakov, Moscow, 1907. It is white's move. What should he play?
This position is from Lile Koridze versus Valentina Golubenko, Batumi, Georgia, 2019. White to play and checkmate in 4 moves:
If you manage to solve this sudoku, please add a comment below saying how long it took you. You will need a Google account to do this.
1. ... f6+
At this point, white appears to have resigned. If he had not done so, the game might have continued as follows:
or
The position below is from Carlos Alberto Vinas Guerrero versus Anton Aaberg, Gibraltar, 2007. It is black's turn to play. What is his best move?
Our younger son created this sudoku using a Javascript program which he wrote himself:
A purdonium is a coal scuttle made to look like an elegant piece of furniture. It has a removable metal lining to hold the coal. They were popular in the 19th century. I found the picture below on the Yola Gray Antiques web site:
What is a purdonium?
(1) A musical instrument.
(2) A coal scuttle.
(3) An Australian flower.
(4) A steam engine.
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