In the world of Metsyssisab, there were three kingdoms, ruled by King Owt, King Eerht, and King Ruof.
One day, a fourth, evil king, King Evif, who ruled a small island, looked to control all of the kingdoms. He challenged the three kings to a mathematical challenge. The three kings agreed. If they won, King Evif would flee Metsyssisab. If they lost, King Evif would take control of all their kingdoms. The rules of the competition as stated by King Evif were:
- Each of the three kings were to be given a digital display with 13 parts.
- Each part of the digital display could show as a single-digit number. Each segment could be lit up or turned off. The segments could ONLY show a number, and not anything else.
- The three kings were each to arrange their own individual display so that by lighting up any number of consecutive segments, they could count up to 13. (For example, a solution with too many segments is 10121345611789, because it's possible to light up the numbers 1 through 13 by using connected segments.)
- There was one catch. The sum of all the numbers shown on all of the segments had to be less than 20.
- The kings could not signify numbers by using anything else except the numbers displayed on the segments, and the actual numbers must be displayed, not the sum of or the number of numbers displayed.
The three kings each figured out how to arrange their display to satisfy King Evif's demands, and he left Metsyssisab. Can you?
There is a bit of numerical trickery going on here. I strongly suggest you figure that out first, or you won’t get too far.
Minor Hint #2:
The kings will each have different answers, for a clear reason once you figure out what's going on. What will work for one king won't work for another.
Minor Hint #3:
Take a look at the kings' and the world's name.