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Comment by bumbledraven | Hacker News Reader

I don't see it there: https://archive.org/details/boris-a.-kordemsky-the-moscow-pu...

Do you recall the solution? It seems like a tricky problem. No approach occurs to me aside from a brute force analysis of the 400 year Gregorian calendar cycle, accounting for the complete leap year rules (under which, e.g., 1900 was not a leap year but 2000 was).

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It turns out that New Year's Day is a bit more likely to fall on Sunday than Saturday. To confirm, here's a bit of simple JavaScript that checks a complete 400-year cycle. You can run it in your browser's console:

  const counts = Array(7).fill(0);
  for (let year = 2000; year < 2400; year++) {
    counts[new Date(year, 0, 1).getDay()]++;
  }
  console.log(`Number of Saturdays: ${counts[6]}; Number of Sundays: ${counts[0]}`);

Output:

  Number of Saturdays: 56; Number of Sundays: 58

Note: getDay() returns 0 for Sunday and 6 for Saturday (https://developer.mozilla.org/en-US/docs/Web/JavaScript/Refe...).

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