Sunil Roy and I were strolling down the road – somewhere in Chelsea area with the rest of the family – when he posed an interesting puzzle for me. See if you can get it.

To give everybody a chance, refrain from posting the answer in the Comments section. Send me a personal message and I will put your name up if you solved it.

You have two dices. One has 1 thru 6 painted on its faces like a normal dice. The other has blank on every face. You can write down any integer number 1,2,3… on each of the blank faces of the second dice. You can even leave it blank – which would stand for 0. You are allowed to repeat the numbers (you can have two faces with the same number).

The question is: What numbers would you paint on the six faces of the second dice such that:

(*) When the two dice are rolled together, the sum total of the two faces up can be any integer between 1 and 12 AND
(*) The probability of any of those integers (meaning the sum of the two faces up being 1 or 2 or 3… or 12) is exactly the same.

You can assume that the two dices are unbiased. (It will be completely random which face will show up)

First ever – a perfect month! All the three circles completed… every single day of the month.

One of those letters for digits… with a twist.

Look at the long multiplication below. As you see, a three digit number DEB is being multiplied by a two digit number DG to give a four digit number AECE. Each letter stands for a digit.

Here is the twist though: A letter above the black line (in red color) if also found below the black line (blue color) is not going to have the same value but will be off by one from each other. Of course, above the black line, any letter, if found twice will have the exact same value. Likewise below the black line. The twist comes only if the same letter comes both above and below the line.

As an example, the two D’s will have exactly the same value since they are both red. But the red G and the blue G are going to be off from each other by one since they have different colors. (If one is 6, the other can be 5 or 7).

The only digits used in this problem are 0,2,3,5,6,8 and 9.

Can you find out what the letters stand for above the black line and below the black line?

There is a wine glass filled with 1000 spoonful of wine. There is a water beaker with 2000 spoonful of water.

You take a spoon of water from the beaker and put it in the wine glass and mix it thoroughly. Then you take one spoon of the stuff (mostly wine with a little water) from the wine glass and put it in the water beaker and mix it thoroughly.

You do the whole thing over again. And one more time (so total of three times).

Of course increasingly the water beaker is getting more wine and vice versa.

Question is at the end of the third full round, do you have more wine (by volume) in the water beaker or more water (by volume) in the wine glass and by how much?

Here is a tougher version… what if after the above three cycles, you did the water beaker to wine glass one more time and stopped? (You did not do the wine glass to water beaker to complete the cycle; essentially three and a half cycles). Now, do you have more wine (by volume) in the water beaker or more water (by volume) in the wine glass and by how much?

Instead of putting your answer (and how you arrived at it) in the Comments section, write to me directly in messenger.

You might have heard various variations of this problem before.

You have 2 ostrich eggs in your hand (fairly hard shells) and you are in front of a 50 story building. The basic challenge is to figure out which is the floor from and above which the eggs will break on impact to the ground when you drop them from a window of that floor. Of course, this can be done with only one egg. You start with first floor – if it does not break, go to second floor. And keep doing this till you find the floor where it does break. The minimum number of tries you will need to guarantee finding out that floor is 50. (Basically, in the worst case, you have to keep trying all the way to the top)

But you have 2 eggs. Now, the challenge is to find out the minimum number of tries with which you can guarantee finding out that threshold floor at or above which an egg will break (one try means one dropping of an egg). Needless to say, once an egg breaks, you cannot use it again.

In a remote part of an African jungle once lived a bunch of lions. No other animal ever came there. Except one day, somehow a deer showed up. Of course, the lions immediately wanted to eat it. Now, these lions were very smart and very courteous. Some might even say they took special “pride” in it 🙂

Puns aside, here are the rules of the puzzle:
(*) the lions have an understanding that only one lion – whoever is first to touch – can kill and eat a deer. (when one attacks, nobody else does; that is where the courteous bit comes in)
(*) they also know that this deer has a property that whichever lion attacks and eats it, itself becomes a deer the next day (which can be attacked and killed by other lions then)
(*) Every lion is desperate to eat a deer. They are okay to live the rest of their life as a deer itself – but will not do so if they know they might get killed the next day by the lions.

Question: Will the deer survive?

Two students independently come to the library every day after dinner between 7pm and 9pm. Each stays for exactly one hour and then leaves. At any night, what is the probability that they met? (meaning that both were in the library at the same time even if for a very short while)