12 years back, on my way back home from DC, I used to post a puzzle almost every week. Doing the same today.

A little background… This week, in Chicago, Deval gave me a little gift. Apparently, she was in a store that sells calendars and came across a calendar that a math problem for each day. Somehow I came to her mind!!

And this is the first problem I saw on the cover page.

You remember mod right? It is the remainder remaining after you do a division. So 27 mod 6 would be 3.

The puzzle is:

15¹¹³ mod 113 = ?

I found this while reading some website.

As you see, there is a quadrant and within that there is a circle that touches one axis. The line that is parallel to that axis and is a tangent to the circle is 12 cm.

Question is what is the area that is shaded? (basically, the quadrant area sans the circle)

… but here is one if you want to try.

A and B are identical squares. C and D are squares too. The only measurement you are given is that the line going from where A&B meet to where C&D meet (the dotted line) – and that is 4 units. The question is what is sum of the areas of C and D (shaded areas).

From the picture you may be able to see that it is raining heavily. Sitting in my balcony, I can see the rain drops hit the parking lot surface in the light that is reflected there.

Here is a question that flashed thru my mind. How many raindrops does the earth get? Millions? Billions? Trillions?

To get started, let’s say it rained in Alpharetta (say 25 square miles) this morning for about 4 hours. How many raindrops did we get?

First take a guess. Just guess how many zeroes (or digits) will be there in that number.

Now, try to do the math. Make whatever assumptions you need to. (And they will differ from person to person). What number do you get? How many digits?

How close were you?

This evening, Sharmila and I were walking around Avalon looking for a bar to sit down for a drink. She realized she needed to pick up something from the grocery store. So, we stepped into the Whole Foods.

I was inside a grocery store after a long time. So, as she shopped, I just ambulated thru the aisles – rather desultorily, if I may add – glancing thru all the different kinds of things they had stocked.

It is then that I came upon this board. I get “Water”, “Bottled Tea” and “Sodas”. But what is “Functional Beverages?”

Is it not really a beverage but just functionally so? Does that mean water, bottled tea and sodas are not functional?

Do you know?

Somebody explain this to me… This was in downtown Burlingame, CA. I was waiting for my friend to show up for dinner. While strolling up and down the street, I caught notice of something peculiar. The parking time restriction was 24 minutes! 24 minutes???

I looked up the internet. Sure enough, downtown Burlingame as parking restrictions of 24 minutes, 2 hours and 4 hours!

Why 24 minutes? Why not 20 or 30 and call it even?

Does anybody know?

Here is another question that has bewildered me (like that “Enter Only” sign that I wrote about before).

Every morning, before daybreak, I come out and sit in our balcony with my cup of tea. It is very calming to watch the early morning walkers and runners occasionally go by in the relative quietness of the dawn. And then, ever so often, a mail truck pulls up in the post office in front of our house and goes thru the exact same steps every day. It is fun to watch how the eighteen wheeler that shows up around 6:05 will go all around the parking lot after loading/unloading instead of exiting directly. And that is to give itself a lot of maneuvering space at the turn for exit.

On a Sunday like this, usually there is no activity in the post office. You can see many of the mail vans sitting idly in the lot. And that brings me to my question.

Check out the zoomed in picture of the vans. Do you notice how every single mail van has on the roof – what looks like a rusted out brown patch – on the right front (as you face the van)? The patterns are very similar too (the sizes vary a little). Now this being a mail van, this is the non-driver’s side.

For the life of me, I cannot surmise why does each and every mail van have that patch on the roof? Does anybody know?

Every time I go out to boat, this sign as we enter the parking lot confuses me. Do you see the problem? I am coming along the road (which is one way anyways) and then I see this sign as I enter the lot. What is the big point putting a sign “Enter only” on my side? What else can I do?

I understand that sign being on the other side to warn anybody attempting to come the other way that you cannot exit there – it is an entrance only point. But why for me?

Never quite figured that one out.

This morning, around quarter to ten, I was doing a quick check of the stock market when something caught my eye.

Note that the Dow graph shows that it has been going down since market opened. And yet, inexplicably, it was green in color. (should have been red). Even better, you can see that just above the graph, it shows that Dow has been up by over 300 points at that point of time.

I guess I should not complain as long as the market is doing well. But still, I can’t explain this.

Can you?