# Geographical statistics

Today I received a list of what looks like random letters and numbers, divided into 6 separate groups. I'm told they are some kind of geographical statistics. Can you figure out what it's about? And what are the missing numbers in Group 2?

## Group 1

GEM: $\{0.71,0.29,0.29,0.29,0.57,0.57,0.57,0.43,0.57\} -> 0.86$
W: $\{0.33,0.33,0.33\} -> 0.67$
KE: $\{0.57,0.57,0.57,0.14,0.57,0.43,0.29\} -> 1.00$
: $\{0.43,0.29\} -> 0.57$
E KGM: $\{0.31\} -> 0.31$
GEECE: $\{0.33,0.33,0.33,0.00\} -> 0.83$

## Group 2

$\;$KE: $\{0.30,0.20,0.80\} -> 1.00$
Q: $\{0.25,0.75,0.50,0.75,0.50,0.75\} -> 0.75$
E B EMES: $\{0.17,0.56\} -> 0.67$
CMB: $\{0.50,0.25,0.38\} -> 0.75$
KMES: $\{???\}->???$

## Group 3

BSW: $\{0.50,0.38,0.38,0.63\} -> 1.00$
SEEG: $\{0.29,0.29,0.57,0.71,0.43\} -> 1.00$
MCC: $\{0.00,0.14\} -> 0.14$
S EE: $\{0.36,0.45\} -> 0.64$

## Group 4

EEE: $\{0.33,0.33,0.22\} -> 0.56$
CMB: $\{0.25,0.50,0.00,0.38\} -> 0.75$
CE: $\{0.20,0.40,0.40\} -> 0.60$

## Group 5

MEC: $\{0.33,0.33,0.33\} -> 0.50$
CG: $\{0.33,0.56\} -> 0.89$

## Group 6

S: $\{\} -> 0.00$

• Are the following features deliberate? (1) Fourth entry in group 1 has nothing before the colon. (2) First entry in group 2 begins with whitespace. – Gareth McCaughan Feb 9 '17 at 19:09
• @GarethMcCaughan: Yes. – Levieux Feb 9 '17 at 19:13

## 1 Answer

Notice first that

the things before the colons are country names with all letters whose alphabet-indices (A=1, ...) aren't prime removed. So e.g. GEM is GERMANY, E KGM is UNITED KINGDOM, etc. (Well, first you suspect that they may be country names with some letters removed. Then you get a list of country names and look for things containing, e.g., E KGM in them. Then you make a list of what letters are sometimes in and what letters are always out. Then you notice what they have in common.)

The numbers

appear to be (2-digit approximations to) nice simple rational numbers. In some cases the denominators may match the number of letters in the country names. This is consistent enough that I think any deviations from this rule are errors, probably mine.

This yields (in ambiguous cases I have boldfaced the one I think most likely, where I have a strong opinion; there are several suspect lines, and I suspect I have been working from an incomplete list of country names):

Group 1:

GERMANY or GUATEMALA: {6,2,2,2,6,6,6,3,4}/7−>6/7
NORWAY or RWANDA or TAIWAN: {2,2,2}/6−>2/3
KENYA or TURKEY or UKRAINE: {4,4,4,1,4,3,2}/7−>7/7
FINLAND [see below]: {3,2}/7−>4/7
UNITED KINGDOM: {4}/13−>4/13
GREECE: {2,2,2,0}/6−>5/6

Group 2:

NORTH KOREA: {3,2,8}/10−>1
IRAQ or QATAR: {1,3,2,3,2,3}/4−>3/4
UNITED ARAB EMIRATES: {3,10}/18−>12/18
CAMBODIA or COLOMBIA: {4,2,3}/8−>6/8
TURKMENISTAN: {???}−>???

Group 3

BOTSWANA: {4,3,3,5}/8−>8/8 SENEGAL: {2,2,4,5,3}/7−>7/7
MOROCCO [uh-oh, letter-count mismatch]: {0,1}/6−>1/6
S EE [uh-oh, I can't find a match for this; could it really be SE EE or something? SIERRA LEONE is SE EE and has the right number of letters and -- see below -- the right numbers]: {4,5}/11−>7/11

Group 4

VENEZUELA: {3,3,2}/9−>5/9
CAMBODIA or COLOMBIA [uh-oh, letter count mismatch]: {2,4,0,3}/9−>7/9
CHILE or FRANCE or ICELAND: {1,2,2}/5−>3/5

Group 5

MEXICO: {2,2,2}/6−>3/6
NICARAGUA: {3,5}/9−>8/9

Group 6

AUSTRALIA or AUSTRIA or HONDURAS or LAOS or SPAIN or SUDAN or SYRIA or TUNISIA: {}−>0

"Empty" countries:

Andorra, Fiji, Finland, Haiti, India, Iran, Italy, Japan, Jordan, Latvia, Lithuania, Nauru, Palau, Poland, Thailand, Tuvalu, Vanuatu.

Of these,

the ones in Europe (which seems likely to be the meaning of group 1) are Andorra, Finland, Italy, Latvia, Lithuania, Poland. We need one with 7 letters and 2 neighbours, so Andorra it is.

It looks as if the groups are

continents, excluding Antarctica which doesn't exactly contain any countries. So 1 is Europe; 2 is Asia; 3 is Africa; 4 is South America; 5 is North America; 6 is Australia.

Perhaps

after clearing denominators, the numbers in {} are the numbers of letters various things have in common with the country names, and the numbers after -> are the total number from all those things together. (Note that the number after -> is always at least the max of the numbers in {} and at most their sum.) What are the "various things"? Well (e.g.) Australia has none and Germany has nine, and those happen to be the number of countries bordering them. Does this work in general? The UK should have exactly one, namely IRELAND, with four letters in common. That checks out. Let's try another country at random: Venezuela is next to Colombia (LA), Guyana (UAN), and Brazil (AZL) so 2,3,3 and a total of LANUZ=5. Yup.

Let's try some other examples.

Iraq neighbours Iran (3), Kuwait (2), Saudi Arabia (3/7), Jordan (2), Syria (3), Turkey (1). Those were clockwise; if we start in Turkey (at the north) and run anticlockwise we get the order shown. On the right-hand side, 3 is the number of letters of IRAQ that get covered. Seems to work; let's try another. Mexico neighbours the United States (EI:2), Belize (EI:2), Guatemala (ME:2). Total: MEI, 3.

So it seems the rule is:

Look at all the country's neighbours, anticlockwise from the north. For each, count the distinct letters in common between the names and list them in {}. After the ->, the total number of letters in the country shared with at least one neighbour. Then divide them all by the number of letters in the country name.

And the missing numbers in group 2 are

for Turkmenistan. That would be: Uzbekistan (8), Afghanistan (5), Iran (4), Kazakhstan (5), covering all the letters of TURKMENISTAN. So {0.67,0.42,0.33,0.42}->1.00.

Remaining mysteries:

S EE (this is probably meant to be SE EE, for Sierra Leone); MCC whose denominators look wrong, CMB in group 4 whose denominators look wrong (these two might be miscounting by the setter?).

Thanks to

Maria Deleva for suggesting that the groups are continents; M Oehm for spotting VENEZUELA, which led me to notice that my lists were compromised by having failed to remove Zs, and for correcting my goof in ignoring the leading space in NORTH KOREA. And Levieux for pointing out my N-blindness when trying to make sense of VENEZUELA. And Peter Taylor for pointing out my idiocy regarding Finland and Andorra.

• the groups are different continents, I believe. – Maria Deleva Feb 9 '17 at 19:34
• EEE is Venezuela. – M Oehm Feb 9 '17 at 19:37
• Continents sounds very plausible. Venezuela too. ... AH! I somehow failed to remove Zs. – Gareth McCaughan Feb 9 '17 at 19:40
• In the third group SE EE - could be Sierra Leone – Maria Deleva Feb 9 '17 at 19:43
• Ah, my bad. So another search led me to Saint Helena. – Maria Deleva Feb 9 '17 at 19:48