Number Circle #1

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• SamuRai constructor · 2024-06-16T17:36:33.041Z

  Here is my solution. There are other means to reach the result: 1A gives that the number ends in 5 (multiple of 5 but not 2) so the lower left is 5 and the digits add to a multiple of 9 (as is true for all multiples of 9). 3A is then a number that is between 5000 and 5999 so it is the square of 71 to 77. Of these only 72 and 75 will be divisible when squared. This yields either 5184 or 5625. 1D is then either 1548 or 6552. Of these only 1548 has all the letters except C in its Roman numeral representation. FWIW 6552 is too large to be represented with Roman numerals but would still be missing X and V if it weren’t.

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• SylveonSoulmate 🤓4:00 · 2024-06-17T04:54:10.779Z

  Very fun! My solve path used the digit 5, then checked 313*(prime^n) until 10000, and narrowed it down with the roman numerals, as the tens place has L, meaning it is from 4-8.

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  • SamuRai constructor · 2024-06-17T12:19:23.235Z

    I think it is possible to solve with any three of the four clues but haven’t taken the time to prove this.

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• Account 🤓2:11 · 2024-06-17T08:48:51.466Z

  Very nice! I figured out pretty quickly that the 5 was needed and then went hunting for the other prime in 2D. In retrospect, 1A means it has to be 3, narrowing the number down to one possibility.

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  • SylveonSoulmate 🤓4:00 · 2024-06-17T09:37:55.019Z

    This is a good idea! I also did not realise I did not need to check that many primes.

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  • SamuRai constructor · 2024-06-17T12:17:51.168Z

    I did try to make this one easier in difficultly since it is the first puzzle of its type. I wanted to make all the clues clockwise and have one start from the lower right square, but there was no way to do this as you can’t clue a entry of length one.

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  • Sendhil Revuluri 🤓5s · 2024-06-19T12:47:55.287Z

    Ah! Excellent point. Divisibility FTW!

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• The Noah 🤓1:15 · 2024-06-18T13:10:04.761Z

  I had a different solve path: 1D gave (x5xx) where x=/=0, because we have a 500 and no 100s (D and no Cs). 2D Checked multiples of a prime and 313 that fit (xx5x). The lowest one was correct!

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• The Noah 🤓1:15 · 2024-06-18T13:21:53.511Z

  https://crosshare.org/crosswords/B42geD1Ieyc1M2SMxIaF/samurai-inspired-crossnumbers

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• Sendhil Revuluri 🤓5s · 2024-06-19T12:47:11.733Z

  Very nice! Thanks for the correction via DM (I had missed powers of primes as a possible answer to 2CW). The time is funny because I definitely spent a LONG time on this on paper and in Google Sheets!

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• OS 1:04 · 2024-06-24T11:20:13.996Z

  Pretty cool but I think the 313 hint is a bit too powerful - after using clue 1 to find the lower left digit the 313 hint narrows it down to 2+ possible numbers (could be a few more but definitely less than like 4 or 5) which are fairly easily checked, the other 2 clues kinda don't come into play as much. Would love to see this concept further expanded though!

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