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Numbers #3 - Base-ics

· Por quatrevingtneuf · Publicado 2024-07-05T04:41:32.777Z

Constructor's Note
In this puzzle, each clue is in a distinct whole number base. Enter each answer in the same base as its clue, using the digits 0 to n-1 for base n.
Comprobando datos de juego anteriores…

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  • ZohMyGosh 🤓33s · 2024-07-05T07:16:01.108Z
    Spectacular stuff.
    • SamuRai 🤓47s · 2024-07-05T09:04:40.334Z
      Solid puzzle. Drop a comment in with the base used for each answer for those who struggled. You’ve got a knack for the pure math puzzles!
      • quatrevingtneuf constructor · 2024-07-05T14:08:30.193Z
        Thanks for the solve! And yes, good idea - I’ll write it up.
      • SylveonSoulmate 🤓5:14 · 2024-07-05T13:23:48.761Z
        Tough but fun!
        • quatrevingtneuf constructor · 2024-07-05T14:41:30.163Z
          Here’s the list of the bases used for each clue:
          • 1A: base 6; 1001 - 234 = 323; (217 - 94 = 123)
          • 4A: base 4; 1101 / (1 + 1 + 0 + 1) = 123; (81 / 3 = 27)
          • 5A: base 2; 10 + 10 = 100; (2 + 2 = 4)
          • 1D: base 5; 14 x 14 = 331; (9 x 9 = 81)
          • 2D: base 3; 11! = 220; (4! = 24)
          • 3D: base 8; (3 + 3)^3 = 323; (3 + 3)^3 = 216
          In general, a helpful strategy is to list out the possible entries for each clue in several bases to see what lines up. Some additional helpful pointers:
          • 5A must be either 020 or 100, so that gives you one digit right away
          • The factorial clue must be a small base, since the number of digits in a factorial increases rapidly. This is enough in conjunction with 5A to solve both clues.
          • The value of 3D is known since it’s only single digits in the clue (decimal 216); it must be at least base 7, or else it has too many digits
          • Similarly, 4A is guaranteed to be divisible by 3, which helps to narrow down the base
          • 1D is actually quite constraining; once 5A is solved, it should confirm this base as well
          Thanks everyone for solving! This was fun to make and I hope to do more like this sometime!
          • dilly 🤓43s · 2024-07-05T14:59:31.494Z
            Whew, another good one, thanks!
            • The Noah 🤓57s · 2024-07-05T23:17:01.290Z
              • The Noah 🤓57s · 2024-07-05T23:15:58.769Z
                Fantastic!! 12/12 in octal
                1A
                1001 - 234
                1
                2
                3
                4
                5
                Horizontales
                1. 1A
                  1001 - 234
                2. 4A
                  1101 ÷ (1 + 1 + 0 + 1)
                3. 5A
                  10 + 10
                Verticales
                1. 1D
                  14 x 14
                2. 2D
                  11!
                3. 3D
                  (3 + 3)^3
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