# Listen With Others

## Listener No 4634: Latin Primer by Nipper

Posted by Dave Hennings on 11 Dec 2020

This week we had the second new mathematical setter of the year, following on from Pandiculator’s Space Invaders puzzle back in May. It was obvious from looking at Nipper’s puzzle that he didn’t understand some of the basic rules: there were no clue numbers, double unches galore and a positively puny set of clues!

What’s more, everything was entered in Roman numerals.

It turned out to be great fun.

Every entry had to end in I, IX, IL, IC, ID or IM and the long entries probably had to begin with C. Starting with the last clue s + b = t + a (F in my notes), s and t were 283 {CCLXXXII}, 337 {CCCXXXVII} or 373 {CCCLXXIII}. From the preamble, they occupied the 9-digit entries. A bit more analysis resulted in their being 283 and 373 in either order with b and a being 101 {CI} or 11 {XI} and going in the 2-digit entries.

Of course, the one bit of sneakiness that we were fed was about {M} and {D}. There were two {D}s and one {M} and they appeared in three entries. I initially assumed that they were three different entries, although part of my brain was on the look-out for their sharing an entry. A bit of analysis would have perhaps made 15ac (damn this lack of numbers!) an entry that could have begun {MD…} but I had to wait for a slight dead end before embarking on that route.

As I have said, it was good fun and, for me, not a particularly quick solve. It took most of one afternoon. Elap had A Roman Puzzle back in 2003, although entering Roman numerals wasn’t specifically mentioned in the preamble. Mind you, it did have clue numbers, no double unches and a lot more clues!

Very enjoyable. Thanks, Nipper.

1. ### Alan Bsaid

Dave, thanks for your blog. A couple of points:
1. All primes must end in I or IX, as Nipper said in the setter’s blog. In fact the only possibilities are I, III, VII and IX.
2. Neither you nor Shirley mentioned how you worked with prime numbers in the required range of those that could possibly fit in the grid (bearing in mind the M and D limits). There are just over 300 such possible primes. I decided that I needed a full table ordered (1) by value and (2) by length of number in Roman numerals, and by value within that. It took me a good 20 minutes to do that initially (using a spreadsheet), including fiddling around with the page layout and type size. Those lists were, for me, indispensable for solving this puzzle, and I found I could crack it quite quickly, although it still took me a while to complete using equation 2.
It was a super puzzle – very different from Pandiculator’s but just as enjoyable.