# Functions and their Codewords

f(x,y,z) and g(x,y,z) are two functions where x and y both lie in the range [1,24].

Complete the table:

Function Codeword
f(12,7,9) Guatemala
g(12,17,8) Khartoum
g(12,21,7) Thimphu
f(13,17,8) Honduras
f(13,19,7) Vanuatu
g(13,19,8) Funafuti
g(13,22,8)
f(16,7,8) Ethiopia
f(16,21,11) Philippines
f(16,23,11)
• Is the codeword the value of the function? Commented Sep 6, 2022 at 6:16
• @msh210 Yes. You have to decode how the codewords are related to their functions. Commented Sep 6, 2022 at 7:21

The functions work out as follows:

x and y represent the positions of letters of the Greek alphabet where the letters used to spell their names also appear among the letters of the name of the country or capital being generated;

z is the output length;

f() generates a country, while g() generates a capital

To demonstrate...

f(12,7,9) Guatemala = country, MU+ETA, 9 letters long
g(12,17,8) Khartoum (Sudan) = capital, MU+RHO, 8 letters
g(12,21,7) Thimphu (Bhutan) = capital, MU+PHI, 7 letters
f(13,17,8) Honduras = country, NU+RHO, 8 letters
f(13,19,7) Vanuatu = country, NU+TAU, 7 letters
g(13,19,8) Funafuti (Tuvalu) = capital, NU+TAU, 8 letters
f(16,7,8) Ethiopia = country, PI+ETA, 8 letters
f(16,21,11) Philippines = country, PI+PHI, 11 letters

Which means our missing two are:

g(13,22,8) Chisinau (Moldova) = capital, NU+CHI, 8 letters
f(16,23,11) Philippines = country, PI+PSI, 11 letters - again!

• How did you figure this out? Commented Sep 6, 2022 at 18:13
• @MadPhysicist Spotted the significance of z just by counting, then looked for commonalities that might explain why the top 3, middle 4 and bottom 3 would have the same x values. Started to spot common letters between the words and realised what they were spelling out. Then checked the alphabet in question and noticed the correspondence with the numbers, tried applying it to the y value too, and it all came together :)
– Stiv
Commented Sep 6, 2022 at 19:11