Euler Squares - Numberphile
Numberphile・13 minutes read
The puzzle involves arranging cards in a grid to ensure each row, column, and diagonal contains specific cards and suits, similar to Sudoku. Mathematicians have debunked Euler's claims of impossibility for certain grid sizes, showcasing the complexity of grid arrangements and challenging established notions in mathematics.
Insights
- The puzzle involves arranging playing cards in a grid so that each row, column, and diagonal contains one of each card and suit, similar to Sudoku but with multiple solutions possible.
- The concept of Latin squares, Greco-Latin squares, and their application in experimental design showcases the puzzle's broader mathematical significance and how advancements in computing have challenged previously accepted mathematical conjectures, highlighting the evolving nature of mathematical problem-solving.
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Recent questions
What is the puzzle involving Aces, Kings, Queens, and Jacks?
A grid arrangement with specific card and suit requirements.
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Summary
00:00
"Card Grid Puzzle: A Mathematical Challenge"
- The puzzle involves arranging Aces, Kings, Queens, and Jacks in a 4x4 grid so that each row, column, and diagonal contains one of each, along with a club, heart, spade, and diamond.
- The puzzle resembles Sudoku, with multiple solutions possible.
- Swapping cards in rows and columns is necessary to achieve the desired arrangement.
- The puzzle is akin to a Latin square, where four objects must appear in each row and column.
- A Greco-Latin square involves two Latin squares superimposed on each other, ensuring every combination occurs once.
- The concept is used in designing experiments to eliminate biases and allow fair comparisons.
- The puzzle works for 3x3 and 5x5 grids but is impossible for 2x2 due to size constraints.
- Euler attempted to solve the 6x6 puzzle but concluded it was impossible, a conjecture proven by Gaston Tarry in 1901.
- Raj Bose later disproved the impossibility of 22x22 grids, showcasing Euler's error.
- With the aid of computers, mathematicians constructed examples of 10x10 and 22x22 grids, debunking Euler's initial claims and labeling them as "Euler Spoilers."
13:21
Challenging Euler: New Grid Possibilities Unveiled
- It is now possible to construct supposedly impossible grids, with only 2 and 6 being impossible due to their size, while 3, 4, and 5 work. This challenges the notion that even great mathematicians like Euler can be wrong, emphasizing the complexity of certain numbers in grid arrangements.
