Sunday Times Teaser 3105 – Roman Primes
by Peter Good
Published Sunday March 27 2022 (link)
Romulus played a game using several  identical six-sided dice. Each die face shows a different single-character Roman numeral. He rolled two dice and was able to form a prime number in Roman numerals by arranging the two characters. Romulus rolled more dice and, after each roll, formed a prime number with one more character, rearranging the sequence as needed, until he could no longer form a prime number less than 100. He was using standard notation where a character before another that is 5 or 10 times larger is subtracted from the larger one, eg, IX=9.
After playing many games he realised that there were exactly three primes less than 100 that could not occur in any of the sequences.
In decimal notation and in ascending order, what were those prime numbers?
 The word ‘several’ here is not intended to impose or imply any limit on the number of available dice.