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Crossnumber Sudoku #2: Alien Math Edition

◆ · By SamuRai · Published 2024-07-15T03:23:31.008Z

Constructor's Note
This is a downs only sudoku crossnumber. All answers are created from the digits 1 through 6. Per sudoku rules, each digit 1-6 appears exactly once in each row, column, and section, I.e. all sudoku rules apply. Only the downs are clued but due to the sudoku constraint, you needn’t solve all the clues. Finally, this is clued using math facts about the numbers (with one exception).
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Comments

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  • Account 🤓9:45 · 2024-07-15T05:20:15.227Z
    Okay, it's the more disappointing option. The pattern completely breaks after 28.
    • SamuRai constructor · 2024-07-15T09:00:46.235Z
      The sum of the first k even numbers is k^2+k. This does force some interesting sub-patterns but not the one I suggested. For example, when k is 2^n-1 (all 1s in binary) the sum is 4^n-2^n which is a 1 followed by n-1 zeros then a 1 followed by n zeros. For those interested, here is a list of the first 50 terms of the summation of even numbers in binary.
      • Account 🤓9:45 · 2024-07-15T14:36:35.616Z
        For completeness, the pattern you suggested was 2^k/3. Not the most interesting pattern, but it still has a lot of interesting things going on.
    • Account 🤓9:45 · 2024-07-15T05:15:12.607Z
      I don't know if 19D is actually a property of triangular numbers or if it's just the Strong Law of Small Numbers... But you have me really curious. For every triangular number I've checked so far, it's either a single string of 1s or alternating digits. (The sum that you described is just double a triangle)
      • kurtalert 1:48 · 2024-07-15T15:46:00.170Z
        Damn, got the digits flipped around in 5D, wasn't reading the question right. Fun - lots of math things in here that I've never heard of before.
        • SamuRai constructor · 2024-07-15T16:42:34.585Z
          I’m hoping the links were educational in that regard and the need to not solve every clue was sufficient. I’m thrilled you enjoyed it.
          • The Noah 🤓15:10 · 2024-07-16T01:07:58.317Z
            The links were a good addition. Made me feel less like I’m cheating to look up new math trivia
        • The Noah 🤓15:10 · 2024-07-16T01:05:33.700Z
          FANTASTIC!! Great fun to solve! I rate it n/10 where n is the number of primes less than 4 factorial :)
          • SamuRai constructor · 2024-07-16T02:31:44.186Z
            Ugh, you expect me to do math! The solution to this problem is left as an exercise for the reader.
          Play today's daily mini crossword
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          Across
          1. 1A
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          2. 4A
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          3. 7A
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          4. 8A
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          5. 9A
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          6. 12A
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          7. 15A
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          8. 16A
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          9. 17A
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          10. 20A
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          11. 23A
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          12. 24A
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          Down
          1. 1D
            Number of equilateral triangles that are formed by the sides and diagonals of a regular six-sided hexagon.
          2. 2D
            The highest number for which prime numbers are one-third the integers from 0 to it.
          3. 3D
            Magic constant for a 5x5 magic square of 1 to 25.
          4. 4D
            The smallest positive even number such that neither one more nor one less is prime.
          5. 5D
            The smallest number xy (where x and y are digits) such that y^x - x^y is larger than 💯.
          6. 6D
            The largest number n such that k^2-k+n generates prime numbers for all positive integers less than n. The largest of Euler’s lucky numbers
          7. 9D
            The number of ways to partition a set of five elements.
          8. 10D
            Maximum number of pieces a pancake can be cut into using nine strait cuts. Lazy Caterer’s number
          9. 11D
            Fewest dots that can be used to form a solid Star of David., aka a Centered Star
          10. 12D
            First Fibonacci number with consecutive increasing digits.
          11. 13D
            If you start a Fibonacci sequence with its digits, you will regenerate itself in six steps. (e.g. 14 regenerates itself in 3 steps)
          12. 14D
            A square number that when squared keeps itself as the final two digits.
          13. 17D
            Fewest number of dots needed to arrange them in either a square or an equilateral triangle (excluding 0 and 1).
          14. 18D
            Alien Area 👽 (one non-math clue for my ancestors)
          15. 19D
            Alternating digits in binary and the sum of the initial ¿ even numbers. (I think these two properties must be related somehow)
          16. 20D
            Number of ways you can pair up six people.
          17. 21D
            Number of unique orderings four people can finish in a race, disallowing ties.
          18. 22D
            Consider a 3x3 grid of squares with their NE-SW diagonals drawn. This is the number of ways to move from the NE corner to the SW corner, each time moving south, west, or southwest. spoiler
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