This week’s trip is over. Time to leave Florida and start skidding on icy Atlanta roads. Also time for a puzzle.

Many of you are aware that my current job involves catching fraud in online transactions. We of course focus on building systems that can catch maximum amount of fraudulent transactions. However, what you may not know is that an equal challenge in building these systems is making sure that we do not flag the good transactions as fraudulent (and irritate the good customers). This is always a tough balance. This is also called the “false positive” problem. (The test showed “positive” but that is a false result).

Here is a false positive puzzle. A village has only one lab that can perform a particular test for a particular disease. The test, however, is only 98% accurate. So, a patient who does not have the disease will get “you do not have the disease” report 98% time. 2% of the time, it will say (erroneously) say “you have the disease”. Similarly, a patient who indeed is suffering from the disease, will get a “you have a problem” report 98% of the time. The rest 2% time he or she will get a clean chit erroneously.

You also know that 0.5% of the village population has been indeed afflicted by the disease.

Your friend from the village just received a report that he has the disease.

How concerned should he be? What is the real probability that he has the disease?

I found this puzzle today. I have not tried it myself. But I think you will know when you get the right answer. Further, unlike other times, I am writing this to you on my way out of Atlanta as I commence my business trip, not on my return trip. Which means, I may not be able to check answers till the end of day or in flights…
Do send personal messages only and not comments.

Arrange 16 coins in a simple square of 4 coins by 4 coins. Now, remove 6 coins in a way that every row and every column still has even number of coins left.

You can also consider this as a desperate attempt to outsource my query after all search engines failed me.

Okay – for all you English gurus… You know how at the turn of the new year, we often write the wrong year for a few days (the previous year) (e.g. on checks)? There is an actual English word for that. For the life of me I cannot remember it.

What is it?

A few days back, I called up an old friend Anamika to wish her happy birthday and she told me that she was out having lunch with her neighbor who also has the exact same birthday!! That got me thinking about what is the probability of such a coincidence happening. Here is a puzzle from that thought process.

If you are mathematically oriented, try solving it. If not, take a guess and see how it compares with the right answer. My guess is that the guess is going to be much larger than the actual number.

Simply put, what is the minimum size of a class where the probability that there is at least one birthday that is shared by two students is more than 50%?

Put in details, if you have two students in a class, the chance they will have the exact some birthday is 1/365. If a third student comes in, there is a higher probability of two of them having the same birthday. If a fourth student comes in, the probability increases further. At what size of the class do you have a 50-50 chance of a birthday being repeated?

Napoleon was not as short as he is made out to be. In fact at 5′ 6.5″, he taller than an average Frenchman. So, where did the misconception of he being short come from?

This is for my American football fans. In the very first Super Bowl, at the start of second half, Packers had to kick off the ball twice to start the game. Do you know why?

What is the longest English word that does not repeat a letter?

Once before, we had talked about English words which have all the vowels in the proper sequence – e.g. Abstemious. Now can you come up with words that have the vowels in the reverse order? (First u, then o….)

The phrase “two plus eleven” and “one plus twelve” are interesting in that both give “thirteen”. They have another relationship. Can you find out what?

There is a debate on whether “I am” or “Go” is the shortest English sentence. It depends upon whether you believe you have to have a subject stated in a statement. Do you know what is the longest sentence in English language?
I will give you the answer – “Marriage” 😉
Okay, that was not a trivia puzzle. Try the other ones….

So, here I am sitting in a much delayed flight to New York. Hope to take off at some point of time. Time for a quick quiz question. I was discussing this with Sharmila during our date night yesterday. And no, she was not referring to me as king of Hearts… We were talking about cards.

What is the one distinctive feature of King of Hearts (physical feature) compared to other Kings in a deck? Try guessing without seeing the cards. Then look at the cards and see if you find it.

Do not post the answer in the comments section.

If you notice carefully there is another distinctive feature of that card compared to the other three kings. Can you find out what it is?

Not exactly going home – in fact am headed to New York from Boston – but have not posted a puzzle in some time…

Try this…

How many squares can you spot in this diagram (of any sizes)?

It is OK this week to post your answer in the Comments section since you will not be explaining the answer. I will send you a personal message whether you are right or wrong.

Part of an email I got from my good old friend Jyotsna from Singapore:

“Btw your puzzle format on FB was an inspiration to the math teachers at the boy’s school. I had asked the teachers to look at posting puzzles in a forum so that kids can help out each other and gave your puzzles discussion as an example. It is the second week of this discussion on the school forum and the class kids seem to love it!! So you are pretty influential in far away Singapore! :-)”

What started as an exercise to get rid of boredom on a flight back from DC a few years back has certainly had some unintentional – but highly welcome 🙂 – consequences. Thank you Jyotsna!

This puts pressure on me to post the next puzzle. This one is dedicated to the kids in Singapore and elsewhere. And also adults.

(Again, do not post in Comment section; send me FB msg; I will respond)

A few days back, I was cleaning my pool and talking to my another good friend Kuntal over the phone. He had posed a question – “what is the last digit of 19^19 + 99^99”. Over the phone we discussed our answers – he had taken an elegant way to solve it – I had used a short cut.

So let’s try that:

1. What is the last digit of the sum of 19 to the power of 19 added to 99 to the power of 99. (19^19 + 99^99).
And an extension..
2. What is the last digit of
9^9 + 19^19 + 29^29 + 39^39 +……+ 99^99

3. If you have an younger kid – or you are stuck yourself – try with the following simpler version – and then the above two become easier. What is the last digit of 99^99?

Today, my friend Gasan showed me this. I was totally stunned. The question is “What are the top cities by population in the world?”. Not the population of the metro area but just the city proper. (The metro area list is very different) . You have to do this without Googling. I will give you the city names. Can you rank them?
Try it and then check in Google. Or I will post the answers:

Beijing, Delhi, Guangzhou, Istanbul, Karachi, Moscow, Mumbai, Sao Paulo, Shanghai, Tianjin (in China)

Note that the top 4 cities by metro area population – Tokyo, Seoul, Mexico City and New York City do not figure in the above list!!!

I am certainly a little wary of posting a puzzle today lest all my FB friends start wishing me Happy Birthday or something like that 🙂

As always, send me messages in FB and not in the “Comments” section.

How can you get 5 by using only two 2s (and you can use any mathematical operators, symbols etc as many times as you want).

Can you come up with 2 different ways?