This is adapted from a more complicated version submitted by Jared Bronski in “The Riddler”. (Thanks to Matt Mooore who gifted me the book this week).

It is one more of those hats on your head and strategy formulation question.

There are three of you. Randomly a white or black hat is put on your head. Each one of you can see the color of the hat on the other two but not the one that is on your own head.

One by one, you will be asked to guess what color hat you have on your head.

Your options are (*) tell a color – Black or White or say (*) Pass.

At any point, if somebody calls a wrong color – you all lose. But if somebody calls a right color – you all win. And if everybody passes at the end of first round, then you all lose.

What strategy can you formulate beforehand to maximize the chances of winning? And what is that probability?

Read this up in the book “Mathematical Circus”.

You have 2 green balls, 2 yellow balls and 2 red balls. One ball of each color is 11 pounds each. The other ball of each color is 9 pounds each. You have a scale and pan balance. (meaning you can compare the weights of two sides – which is heavier and which is lighter but you never know the exact weight).

What is the least number of weighings required to find out which are the three heavier balls and which are the lighter balls?

Send me personal message with the reasoning.

I have finally been able to memorize all the country names and their capitals. For this purpose, I am defining countries as those 195 that are recognized by the United Nations. Some interesting puzzle questions emanate from that:

Take a guess at these questions and write down if you want in the Comment section. Then check with Google (or wait for a day – I will publish the answers). Do NOT write the answers here AFTER Googling.

1. The smallest number of letters in any country capital is 4. For example: Rome. How many such 4 letter country capitals are there? Can you name them?
2. How many countries have the capital name same as the country name? e.g. Singapore capital is Singapore. How many can you name?
3. Now, some capitals are the same as the country name with the word “City” attached. e.g. capital of Mexico is Mexico City. Similarly, what are the other countries that have the same pattern of capital names?
4. Many countries, during their early ages, had certain cities flourish because of trade – that happened mostly thru sea waters. Thus you will see many of those countries have a port as their capital. Some of them even have the name Port in their capital name. e.g. “Port Au Prince” for Haiti. What are the other capital names that you can come up with that have Port in it?
5. Many capital cities were named after certain Saints. They tend to have names starting with St., San, and so on. How many of them can you come up with?
6. Which are the capital cities that start with the letter “Y”?
7. How about “Z”?
8. Which is the most common first letter for capital names? Meaning more capital names start with this letter than any other letter. There are an astounding 25 of them!
9. A couple of countries have an apostrophe in their capital names. Can you name them?
10. Now the final one: What is the capital (legislative capitals) of Sri Lanka and Myanmar? Hint: I did not realize that they had moved their capitals recently.

My brother in India and I recently started new jobs and we both travel a lot for work. We still find time to talk to each other once a day – even if for a few minutes. Almost all his work related travel is by trains. And mine by planes. This morning, I had called him and I could hear the sound of the train horn in the background. Trains are still something I get terribly fascinated by.

Which got me reading up about railway lines today. Learnt some cool stuff and also realized that so many things I was taught during my school years are not true. Or at least not true any more.

Try these.
a. Which country has the longest railway network (in total miles/kms)? This is something I had to “un”learn!

b. Can you think of the largest country that has no railway? How about the second largest country without any railway? Here is a hint – they are neighboring countries. And the first one used to have a railway in its past. But not anymore.

c. Think about the longest distance you can go without ever having to change trains. Can you guess between which two cities that train would be running?

d. Here is something else I knew wrong. What is the longest railway platform in the world?

e. Which is the busiest station in the world? Can you guess the country if you do not know the station name? More people go thru this station in a matter of weeks than the total number of people that go thru the world’s busiest airport in a year!

f. How about the longest railway tunnel? Can you guess the country if you do not know the tunnel name? It is a rather new one. Has been in operation for only two years.

g. What is the longest railway bridge in the world? Want to guess the country name? It is over 102 miles long. For my friends from Durgapur… that is longer than Durgapur to Kolkata!

h. How about the highest railway station in the world? Want to guess the country name?

i. What is the longest railway station name? I do not expect you to know the whole name – although it has a shortened version – but can you guess which country it is in? The name, roughly translates to “St Mary’s Church in the Hollow of the White Hazel near a Rapid Whirlpool and the Church of St. Tysilio near the Red Cave”

j. Conversely, what is the world’s shortest railway station name? Want to take a guess at how many letters or which country?

Once I finished memorizing all the African countries, I asked myself if I could extend that to learn all the country names in the world. Naturally, I started by Googling “How many countries are there in the world?”

You would think it should be a straight forward answer. Far from it. The definition of a “country” is not as clear cut as I had thought it would be. There are countries that the UN recognizes. Then there are are completely autonomous areas with their own government and no control from outside – but they do not go for UN membership (e.g. Cook Islands). Kosovo is not a recognized country by UN, but it competes in the Olympics as a nation.

In fact, if I have this right, there are 195 sovereign states recognized by the UN, 201 partially recognized states, 204-207 de facto sovereign states, 206 Olympic nations, 211 FIFA countries and get this – 249 countries that have their own ISD (country code for telephone numbers) codes!

Anyways, finally memorized the names of all the nations recognized by the UN. Trying to understand the definition of continents was a trifle more tricky. Learnt some really interesting tidbits about continents. See how many of these you knew:

1. Which continent is Greenland in?
2. Which is the continent with the most number of countries?
3. Which is the continent with the least number of countries?
4. How many countries have contiguous area that straddles over two different continents?
5. This one is specially for my friends who live in the USA like me. How many countries in our continent?

Sunday morning puzzle

I was led to this problem by my great friend Karthik’s son – Aadi – who is a whizkid in logic and numbers problems. I need to spend more time with him just to learn about more puzzles.

This problem was published in New York Times as the Tax Man Problem. I have changed the description a little – but the problem is the same.

You and I sit across a table with twelve cards marked 1 thru 12 between us. Following are the rules of the card:

1. You pick a card.
2. I get to pick all the factors of that card that are remaining on the table.

(To explain, if you picked card marked “10” first, I pick up “1”, “2” and “5”. )

3. We continue with this.

(To explain, now if you pick “8”, I pick “4”. Remember “1” and “2” are already gone in the previous move)

4. You CANNOT pick a card if there are no factors of that card left for me to pick.

(To continue with the above example, you cannot pick “11” now, because its only factor “1” is already gone and I am left with nothing to pick)

5. Finally, when you have run out moves (there is no card left for you to pick without violating Rule 4 OR there are no cards left on the table), the game is over.
6. Now we add up our cards.

Whoever has higher total, wins.

To finish off that example:

You: 10
I: 1,2,5
You: 8
I: 4
You: 12
I: 3,6
You: run out of moves (you cannot pick any of the remaining cards – 7,9,11 – since they have no factors left)
I: 7,9,11

Your total: 10 + 8 + 12 = 30
My total: 48 . I WIN!!

Question: What is the highest total you can get and win?

After studying about African countries (just their location and their names – no more, yet) and Nikita and I doing the jigsaw puzzle every afternoon for fun, finally, I was ready for the test on Sporcle.

In the very first round, managed to name all the countries and their locations. In 4 minutes and 09 seconds. Now I am very scared to try it out again. I am deeply aware of the fact that me score can only go downhill from here 🙂

The 4 minute plus probably is not a stellar time but I am telling you – Africa does not make it easy on you with the country names. It has Guinea, Guinea-Bissau and Equatorial Guinea. I think their Department of Naming Diversity was headed by an ex-Atlantan (we call all our roads Peachtree). There is a Republic of Congo and then to make it more interesting, there is a Democratic Republic of Congo.

Funny part is Gambia – which foresaw that other countries might also call themselves with similar names – made the preemptive move of putting the definitive article in its name. It calls itself “The Gambia”! The kicker? When Portugal ruled it, it was called “A Gambia” !!!

Next round of studies … capitals of all those countries. This is going to be much more difficult since there is unique shapes and locations to visually remember like I could for the countries.

Bill Hubbard, what can I say – 3 different airlines, 6 flights, 4 different cities this week. You know who to blame for one more puzzle 🙂

Anybody who works out the answer, feel free to post the answer only in the Comment section. Send your logic as a personal message to me. Do not write your logic in the Comments section.

Now to the puzzle.

In a Polynesian island, girls are highly preferred as a child. This has led to a strange practice over the years among couples who are trying to have a baby. If they have a baby boy, they keep trying to have another baby in the hope that it will be a girl. If it is a baby girl though, they stop having any more babies. Of course, given any birth, the probability of having a baby boy or baby girl is half and half. So, they keep having more babies as long as they are all boys and stop moment they have a girl

As a result, there are couples who have one girl, couples who have one boy and one girl, couples who have two boys and one girl, couples who have three boys and one girl (and the girl is always the last baby they have) but no couple with two girls (or more).

Here is the question: Over a longer period of time, what is the likely ratio of boys and girls in the island?

In a class there were 40 students with roll numbers 1 thru 40. One day, the teacher got them all to sit around in a circle sequentially in the order of their roll numbers (1 thru 40). (Of course 40 sat next to 39 on one side and 1 on the other). She then gave a wand to student number 1. What the student had to do is turn towards the next student (which would be #2) and tag him/her with the wand. Upon tagging, the tagged student steps back and is out of the game and the wand is then handed to the next student – which would be student #3 in this case

Now student #3 does the same thing – tags student #4 who steps back and is out of the game and then the wand is handed to #5.

This keeps going on and on (in circles) till only one student is left.

Can you figure out which student was the last one left?