This week I have three chess puzzles for you, but you don’t need to know the rules for two of them. These two are variations of the famous Eight Queens Puzzle, which requires the solver to place eight queens on an eight-by-eight chessboard so that no two queens attack each other. The Eight Queens Puzzle requires too much trial and error for my taste, which is perhaps why this problem appears more often in computer science courses as an exercise in writing a program that finds cases for you.
The world of checkers puzzles is full of beautiful and often humorous structures, but sometimes it takes a lot of experience to solve or even appreciate them. The most common type of chess puzzle describes a position and challenges the solver, forcing them to checkmate in a given number of moves. This week’s third puzzle puts an enjoyable twist on this standard genre, instead asking you to find a move that doesn’t result in immediate checkmate. You need to know this rule of chess. As far as chess puzzles go, it’s not terribly difficult, but hopefully gives you a taste of how fun these pieces can be.
Did you miss last week’s puzzle?check it out here, and find its solution at the bottom of today’s article. If you haven’t solved last week’s question yet, be careful not to read too far into it!
Puzzle #25: Chess Puzzle
- The queen attacks all squares in her row, column and diagonal. Place five queens on a five by five chessboard so three The square will not be attacked by any queen. If you want to try the configuration on a digital board, I’ve set one up heresealing off a five by five area with black pieces.
- The knight attacks every square he can reach in the L-shape as follows: two squares horizontally (left or right) and one square vertically (up or down), or two squares vertically and one square horizontally. What is the maximum number of knights that can fit on a standard 8×8 chess board so that no two knights attack each other?
- Find White’s move in the position below no Resulting in immediate checkmate. Karl Fabel, a talented and prolific chess composer, published this book in 1952.
I’ll be back next Monday with answers and new puzzles. Do you know a cool puzzle that you think should be featured here?Leave me a message on Twitter @JackPMurtagh or email me gizmodopuzzle@gmail.com
Solution to Puzzle #24: Recycling the Calendar
Did you solve your problem last week? puzzle timely?
The calendar you are selling does not have the year written on it. If someone wants a calendar for 2024, you can give them a calendar with the correct day of the week for 2024 (January 1st is a Monday, January 2nd is a Tuesday, etc.)
- How many different calendar types would you have to stock to cover all possible years?
- When will people use the 2023 calendar again next year?
- How many years can pass between two uses of the same calendar?
Find out below.speak out peter Snipe them all and call the Gregorian calendar the “Gregi System”.
1. There are 14 different calendars. A year can start on any 7 days of the week and has 365 or 366 days (leap year). This yields a total of 14 possibilities.
2. 2034 is the next time the 2023 calendar will be used again. Every non-leap year, the days move forward by one day. Think of it this way: 2023 starts on Sunday, and every 7 days thereafter, the week resets to Sunday (January 8th, January 15th, etc.). So, starting at number 1 and adding any number divisible by 7 (7, 14, 21, 28, …), you get back to Sunday. 364 is divisible by seven (7 x 52 = 364), so adding it to 1 gives us 365, which is the last day of the year. This means December 31st is also a Sunday, causing 2024 to start on a Monday. This is how all non-leap years work. After a leap year, the days will move forward two days due to the extra day.
With this, we can calculate when the 2023 almanac (a non-leap year starting on Sunday) will return. The date moves forward by 1 every year, except after a leap year, when the date moves forward by 2:
Since 2034 is not a leap year and starts on a Sunday, it uses the same calendar as 2023.
3. The maximum interval between uses of the same calendar is 40 years. If you came up with 28, you’re not alone. I’ll explain why 28 is a natural guess, and then why the gap is actually so large at 40.
Leap years are less common than non-leap years, so it stands to reason that the gap between leap years should be larger. After a leap year, subsequent years will change dates according to the following pattern: 2, 1, 1, 1, 2, 1, 1, 1, etc. (You can see this in the table above starting with 2025). Therefore, every leap year (every four years) moves forward five days (2+1+1+1) from the previous leap year (for example, 2028 is the leap year after 2024 and it starts on Saturday, 2024 five days after Monday of the year). Every four years, starting with a leap year, the date moves forward five times, and you need to do this seven times before you can cycle back to the same starting date. It takes 28 years to experience seven leap years (in fact, 2052 is 28 years after 2024 and the first leap year to start on a Monday).
A huge exception could expand or contract that number. Years divisible by 100 skip leap years (unless they are divisible by 400). 2100, 2200, etc. are not leap years. Consider the calendar year 2072: the leap year starts on a Friday. 28 years later is the year 2100, which also starts on a Friday, but it is not a leap year! We must continue for another 12 years to repeat the calendar of 2072 in 2112.
