Once we
read the kings' and the land's names backwards, it is clear they are using different bases for the solution.
When King Evif
states that the numbers up to 13 shall be displayed, he means eight, as ${13}_5=8_{10}$.
Also, the limit on the sum of digits is ten, as ${20}_5={10}_{10}$.
Possible solutions that fulfill these requirements are:
King Otw:
11101000 for base 2
11101000 = 1
11101000 = 10
11101000 = 11
11101000 = 100
11101000 = 101
11101000 = 110
11101000 = 111
11101000 = 1000
King Eerht:
20112210 for base 3
20112210 = 1
20112210 = 2
20112210 = 10
20112210 = 11
20112210 = 12
20112210 = 20
20112210 = 21
20112210 = 22
King Ruof:
12011013 for base 4
12011013 = 1
12011013 = 2
12011013 = 3
12011013 = 10
12011013 = 11
12011013 = 12
12011013 = 13
12011013 = 20