Here is a 5×4 rectangular wordsearch (space 20) containing the primes between 1 and 100,
{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}
(numbers in any route or diagonal/backwards, overlaps permitted (17 = 7,17,71))
15414
29763
38310
05100
It has a rating of “4” as a result of we have been capable of pack 4 unused zeros in there.
We cannot make a 3×3 wordsearch as there are too many digits as a result of ’11’;
in idea, the very best rating we are able to get is “2” with a 3×4 wordsearch (space 12):
112
345
678
900
But that is lacking primes like “23”, so is invalid.
Without utilizing a pc:
What is the minimal potential space for a legitimate rectangular wordsearch?
For a wordsearch with that space, what’s the highest potential rating you could find?
Provide an instance.
Proof of optimality can be a bonus, by hand (most popular) or laptop (acceptable), however I do not know if a proof past brute pressure exists, so am much less involved with that, though it will be attention-grabbing.
