# Two trips with a common theme

A while ago me and my friend decided to take two different trips to specific nations. I visited four nations and he visited four other nations.

Here are two lists. List 1 is a list of my destinations and an incomplete list of his destinations, both arranged in alphabetical order by the name of the country. List 2 contain four letters with some numbers to the right.

        List 1:
Me: Austria, Republic of the Congo, Scotland, Switzerland

Friend: Hungary, _ _ _ _ _ _ _, Tanzania, _ _ _ _ _

List 2:
Me: M (3rd) (1), D (3rd) (2), A (6th)(1st) (3)(9), S (5th) (4)

Friend: M (2nd) (5), D (1st) (6), A (2nd) (7), S (6th) (8)



What theme were we following?

• I realized some might have been looking for something related to flights or so. Just want to say, it has nothing to do with that. I could just aswell have said "they visited" instead of "took a flight". Let this be a small hint before a stronger hint some time later (if it's still unsolved). Oct 22, 2023 at 11:45

The hidden theme to your journeys is:

OPERATORS!

To find this, we need to look at the four letters that appear in the second list: M, D, A, and S. These form a set...

...when you think of them as the initial letters of Multiplication, Division, Addition and Subtraction, the four chief operations of arithmetic.

Now consider the four countries we know you visited. Specifically...

...their flags:

Note that each of these contains a feature that resembles an operator for one of these arithmetic operations! Austria's central white band resembles a minus ('-'), Congo's diagonal resembles a division slash ('/'), Scotland's cross resembles a multiplication sign ('x'), and Switzerland's cross resembles a plus sign ('+').

For the 'M', 'D', 'A' and 'S' of List 2, we need to consider the name of the country whose flag corresponds to the relevant arithmetic operator, and take the nth letter, as indicated in parentheses. We then arrange them according to the order shown in the second parentheses (note there are 9 unique numbers here, which will help us to spell out a 9-letter answer word). So, "M (3rd) (1)" tells us to take the third letter of your Multiplication country (Scotland) - which is 'O' - and place that in position 1 in the answer word.

Doing likewise for the rest of your list, we extract the 'P' from 'Republic of the Congo' for position 2, the 'E' and 'S' from 'Switzerland' for positions 3 and 9, respectively, and the 'R' from 'Austria' for position 4. This gives us the foundations for our answer word: OPERxxxxS.

We can see what this is likely going to become, and our known information from your friend's list gives us two more letters...

Hungary's central white band (which resembles '-') makes it our Subtraction-related flag, so we take its 6th letter - 'R' - and place it in position 8. And Tanzania's diagonal (which resembles '/') makes it our Division-related flag, so we take its 1st letter - 'T' - and place it in position 6. Our answer word is now: OPERxTxRS. It surely has to be OPERATORS, right?!

We can confirm this hypothesis if we can identify the two missing countries...

One of them must contain a 'Swiss cross' feature for our plus sign (Addition) and have 'O' as its second letter, while the other must feature a 'Scottish cross' for our multiplication sign (Multiplication) and have 'A' as its second letter.

Moreover, one of them must have a 7-letter name and appear alphabetically between 'Hungary' and 'Tanzania', while the other must have a 5-letter name and appear alphabetically after 'Tanzania'.

With these criteria in mind, we quickly find our candidates by consulting lists of countries and flags - Jamaica (which has a 'Scottish cross' on its flag) and Tonga (whose flag has a 'Swiss cross') - and the puzzle is solved!

• Those are the missing two countries and ofc you got the correct theme. Great job! Oct 23, 2023 at 7:40