Longest Roman Year
Read the puzzle
A key shows Roman letter values: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000, with VI = 6 as an example. Four years are listed: 1999, 2028, 1888 and 1777. Which year needs the most Roman letters when written as a Roman numeral?
Which year needs the MOST Roman letters?
Some digits need many letters: 8 is VIII, but 9 is just IX.
1888
1888 = MDCCCLXXXVIII: 13 letters. 1777 needs 10.
How to solve it
Write each year one place at a time: thousands, hundreds, tens, then ones, and count the letters.
1999: M (1000) + CM (900) + XC (90) + IX (9) = MCMXCIX, which is 1 + 2 + 2 + 2 = 7 letters.
2028: MM (2000) + XX (20) + VIII (8) = MMXXVIII, which is 2 + 2 + 4 = 8 letters.
1888: M (1000) + DCCC (800) + LXXX (80) + VIII (8) = MDCCCLXXXVIII, which is 1 + 4 + 4 + 4 = 13 letters.
1777: M (1000) + DCC (700) + LXX (70) + VII (7) = MDCCLXXVII, which is 1 + 3 + 3 + 3 = 10 letters.
The winner is 1888 with 13 letters.
The usual wrong answer is 1999, because it looks like the biggest or most complicated number. In Roman numerals a 9 is short (IX, XC, CM use two letters each), while an 8 is long (VIII, LXXX, DCCC use four each). So 8s make long numerals and 9s make short ones.
Takeaway: count letters per digit. Digit 8 costs 4 letters, 7 costs 3, and 9 costs only 2.
