Number Circle #1

◆◆ · By SamuRai · Published 9 months ago

Constructor's Note

For this mathy puzzle, the clues give a hint to a four digit number read clockwise or counterclockwise starting from clue’s square. No single clue yields a unique number. The clues in combination do however give a unique solution.

Filling out my cross numbers of various sizes. This is the mini-mini 2x2 creation.

侍 SamuRai

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SamuRai constructor · 9 months ago
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.
SylveonSoulmate 🤓4:00 · 9 months ago
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.
- SamuRai constructor · 9 months ago
  I think it is possible to solve with any three of the four clues but haven’t taken the time to prove this.
Account 🤓2:11 · 9 months ago
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.
- SylveonSoulmate 🤓4:00 · 9 months ago
  This is a good idea! I also did not realise I did not need to check that many primes.
- SamuRai constructor · 9 months ago
  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.
- Sendhil Revuluri 🤓5s · 9 months ago
  Ah! Excellent point. Divisibility FTW!
The Noah 🤓1:15 · 9 months ago
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!
The Noah 🤓1:15 · 9 months ago
https://crosshare.org/crosswords/B42geD1Ieyc1M2SMxIaF/samurai-inspired-crossnumbers
Sendhil Revuluri 🤓5s · 9 months ago
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!
OS 1:04 · 9 months ago
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!