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Singapore Math Problem – Cheryl’s Birth date

cheryl logic test

Some days back the above maths problem in Singapore maths Olympiad was being passed around. Here is my solution. And yes, I solved it on my own before confirming the solution from elsewhere on Internet.

Take a look at the 10 possible choices Cheryl gave. Let’s put them in the tabular form

======  |      14   |      15   |    16    |    17    |    18   |     19   |


May         |              |     x      |     x     |            |            |     x     |

June        |              |            |            |     x      |     x     |            |

July         |     x       |             |     x     |             |           |            |

August    |     x       |     x      |            |     x       |           |            |

At first Albert says he does not know, but he knows that Bernard does not know as well. Is it even possible for Bernard to know the birth day just by knowing date? Looking at the table above, it is indeed possible. If the date Bernard knew was 19, it happens only one month in given choices, May. So Bernard could have guessed the birth date just by knowing the date. Same is hte case for date 18. It happens only on June 18.

How can Albert say that he knows Bernard does not know? He can say that only if based on the month he knows, he can eliminate the dates being 18 or 19. That is possible only if the Month is not May or June.

So Albert knows the month is no May or June. So we can eliminate 5 out of the 10 choices.

At this point Bernard says he knows the date. He knows that if Albert is making such a statement, that means the month is not May or June. Now Bernard says he knows the birth day. That means out of the choices left, Bernard can guess the date by knowing just the date. Clearly the date cannot be 14 because it has two possible month choices and Bernard would have to know the month to eliminate one of them.

At this point we know that the Months are not May and June and date is not 14.

Now after knowing this much, Albert says he knows the date. Since he knows only month, it must be a month which has only one possible choice of dates. If the month was August, it still has two possible dates. But if the month is July, then it has only one date.

That is our choice. July 16 is the answer we want.

Mindfulness – Where the Judge Is Guilty

Often times the people who have no introduction with Zen or Upnishadic philosophy struggle to grasp concepts like mindfulness. Often times the discussions revolve around practice and techniques that are very superficial.

Mindfulness and the self inquiry that mostly follows is a radical departure from how you normally use your mind. Normally there is a judge, an ego or an identity. And there is a defendant – the experience of present moment. If the experience is pleasant, the judge acquits the defendant and may even reward it. If the experience is stressful, conflicted, the judge is inquires about the crime and orders appropriate corrective measures.

In mindfulness, the roles are reversed. The experience is validated, is not guilty. The present moment is without blame. No matter whether you are having a stressful experience, negative emotions. No matter if there is a guilt or fear or shame. No matter if it feels like you cannot look at yourself in the mirror.

All is OK. You are allowed to experience it all. You are not required to struggle with it. You are not required to take corrective measures to ensure that the pleasant experience returns as soon as possible.

“I just failed in exam. Should I not take corrective actions?” Someone might ask.

I am not talking about taking corrective actions in physical world. I am taking about taking corrective action to make yourself feel guilty or stressful to motivate yourself to take corrective action in physical world. A part of you beating other part of you will never work right.

This is mindfulness. You can stop here. Or if you want, you can wander into self inquiry.

This beating part, this judge that is brought under lens in mindfulness based self inquiry. ” What laws you are applying? Are those valid?  And by the way, Who are you?”

When this happens, we find something very interesting. Often times the hardest part of the experience is the struggle to fix it, the punishment that was handed to the experience. We operate under the assumption that the struggle is inherent to the experience.

But it doesn’t have to be.

You can feel pain and not struggle with it. And not having to do the struggle gives you a lot of space and lot of spare strength. If you count this in, we all have enough strength to deal with the stuff life throws at us.

But then why do we make a habit of this struggle? A psychology experiment I read comes to mind.

Researchers placed three rats in three boxes. In each box there was a lever to pull and a hole to drop a piece of cheese in.

In the first box, every time when a rat pulled the lever, the researcher dropped the cheese. Very soon rat knew that it can get cheese any time just by pulling the lever.

In second box, no matter what rat did, cheese was never dropped. Very soon the rat realized that nothing happens when they pull the lever. So it stopped pulling the lever.

In the third box, when the rat pulled the lever, the cheese was dropped randomly. The rat couldn’t quite figure out when the cheese drop happens and when it doesn’t. Result? The rat kept pulling the lever even when the researcher did not drop cheese for long time, almost till it fainted.

Intermittent reinforcement. This is how obsessions are formed.

Every now and then the judge and the judgement works in our mind. Every now and then the mental strategies of ego, like fear and guilt produce the desired outcome. That gives a false illusion of control and we keep on perpetually pulling the lever. Perpetually running the lawsuit. Perpetually suing the experience.

A Zen Story – “No One Has Ever Been Enlightened”

A zen student who has been studying zen for long time, goes to a master in far away village for more instruction. The master refuses to let the student in his hut. But the student just sits outside in meditation. He continues to serve the master and bring fruits and water to him.

One day the master comes out and asks the student. “Why are you doing all this work?”
“I want to get instruction from you” replies the student.
“What will you do with more instruction?”
“I want to attain enlightenment.”
“Stop trying to get instruction to attain enlightenment. No one has ever been enlightened.” quips the master.
And at that moment the student gets enlightened.

On face this looks like a dialogue that borders nonsense. But that’s the thing about zen stories. There is always an outright nonsensical component. If you keep focusing on that, you never get the story.

What you need to do is neither think about it, not toss it with ridicule. You need to just let the story be with you. Develop an intimacy with it.

Then one day it hits you.

This is how the story above hit me.

We live in the world of thoughts and emotions and habits, and most importantly, the owner of all of these, a mental structure called ego. Often the passion we use to carry out the worldly pursuits is brought over to carry out the spiritual pursuits as well. The ego wants one more feather in its cap, or one more armor to protect itself against the insecurities.

However all these are mind games and enlightenment is end of these mind games. Just like a ball of butter does not remain a ball of butter when brought close to the fire, an ego, or an identity does not remain an identity when it meets the state of enlightenment. When you are enlightened, you are no one.

This is what the master meant when he said “no one has ever been enlightenment.”

Ancient Nalanda University Comes Back to Life


On Monday 01, Sept 2014, while rest of the India went around their usual business, something extraordinary happened. A moment to be written with golden letters in history of not just India, but that of the world. Because today an ancient institution springs back to life. An institution which once symbolized the culture and knowledge traditions of India, and had a remarkable influence on the very idea of India itself.

Ladies and Gentlemen, after 800 years of break, Today, on Sept 01 2014, classes were conducted for the first time in University of Nalanda. After almost a millenium, the campus is buzzing again with professors, oblivious to the backdrop of frantic construction activity around.

An institution so old in time that in predates Oxford and Cambridge by many centuries. An institution so vast in expanse that it enrolled more than 10,000 students from all over the world, about 1500 professors and staff and more than 200,000 books (hand written, there was no printing), in its nine storied tall library. Wide range of subjects like philosophy, astronomy, mathematics, arts, languages, were taught here.

List of people who visited or stayed at Nalanda sounds like a who’s who, or sort of directory of most influential names in ancient Indian history. It includes names such as Verdhaman Mahavira, Gautam Buddha, Ashoka, Chandragupta, Bramhagupta, Nagarjun, Adi Shankarachayra and so on.

But time is a tide. In twelfth century, Nalanda was attacked and burned by Khiljis. The library burned for days. The students and teachers dispersed in decades to come. A visitor hundred years later found an alone monk Rahul Bhadra conducting classes for about 10 students.

Eventually it all stopped. The dark days began. for the next several centuries the ancient halls slowly crumbled with time as India was colonized by people who did not share the same passion for knowledge.

After independence, Nalanda ruins gained attraction as a tourist destination. The grounds that once witnessed contemplation on the meaning of existence now witnessed hurried chatter of tourists to take pictures. Those few who could imagine the expanse, were still in awe. But the soul of university is knowledge and it wasn’t there.

Until 2006.

Then President of India, Abdul Kalam, floated the idea of reviving Nalanda in 2006. The idea got momentum next year when a group of Asian countries including India, China, Japan, Singapore, and Thailand set up a joint team for the same purpose – reviving Nalanda. The winds of positive change began to blow. Committees were formed, proposals were sent around. Engineers put on their hard hats. Architects got back to drawing boards. Bureaucrats and accountants dug into their balance sheets.

Things began to change for Nalanda.

A decade of efforts showed first fruits on Sept 01, 2014, as the university formally began operations with 11 professors and 20 students, headed by Chancellor Amartya Sen, a Nobel prize winning economist. Initially began on a small scale, the university budget is over 1 billion dollars with major plans to expand soon.

Let’s take a moment to salute Nalanda for this tremendous inspirational journey. Nalanda not only represents a university, but it represents a spirit. Phoenix like spirit. A shining proof that no matter how hard you are stomped, you can always rise again.

Here is new Nalanda university website


(Photograph below is artistic rendering of the proposed plan of new Nalanda campus)


Colonialism – A Societal Abuse

A bit departure today. Into history and politics.

Often times I post on online forums and debates. One recent such debate was about colonialism. The poster was most likely from Britain or one of the other colonizing countries, and was making a point that India and all other colonized nations should not be complaining really because they got a lot out of colonialism. He stopped just short of saying that the colonized countries should in fact be thankful to their colonial masters.

Lots of Indians voiced their disagreement, some in strong words and the argument degenerated. However I had a feeling the real problem was not quite captured. Thus this post.

History is just vast sea of facts. Based on these facts we make our judgments. Why we focus on a particular set of facts and what judgment we derive from them depends on our emotional undercurrents. And sadly, rarely people dig deeper than the superficial facts and judgments.

I have strong negative feelings about British colonization. You know why? Every nation, every society has this ongoing love affair with their past, their history. It is from this love affair that they derive their sense of identity, their pride, their self esteem. It is a form of self worship. Everyone has an altar deep in their mind, and there is an idol of self. There is nothing wrong in self worship as long as you are not sacrificing others at that altar.

The grim reminders everywhere of colonization throw a wrench in this self worship, this love affair with the past. People struggle to feel good about themselves. This struggle for self esteem is very subtle and hard to spot, but very pervasive and thus far more damaging in long term. It creeps into your decision making, it creeps into your relationships, it creeps into your sense of identity. It contributes a lot to create a dysfunctional society.

It’s a trauma. It’s as if part of me wants to forget that trauma because it’s painful. But part of me wants to keep that trauma alive as a reminder, as an insurance that I will be able to avoid such trauma in future. And the conflict tires me out.

In short, I don’t like colonization because it makes me difficult to love myself. And ironically it is difficult for a British person to accept colonization as bad because it makes it difficult for them to love themselves.

For the most part the first world, and especially Anglo Saxon demographics, has been unaware of how a massive societal trauma feels. Some segments of this world, like women experiencing rape or soldiers experiencing PTSD have been exposed to this trauma. But others are blissfully unaware and vastly underestimate the impact such trauma has on your life.

No, 9/11 was still not a national long term trauma. It was painful tragedy, but not long term trauma. Because USA was able to bring people to justice and bring some closure. When you bring closure, you can maintain your self-respect and a sense of control over your surrounding. It hurts a lot more when you are violated but have to live with the trauma and see the perpetrators walk free. We are all aware of dangers in this world. But we live with a certain plausible deniability of “that may not happen to me.” When you suffer trauma, but can’t bring closure, that comfort of plausible deniability is taken away.

Most of the first world nations have this blind spot for trauma. And that sadly reflects in their politics and foreign policy.

Consider the Iraq war. How did it play in Iraqi minds? History reads “America and Britain invaded Iraq and Iraq lost.” No matter what, that reminder of loss and the crisis of self esteem inflicted is going to contribute to the dysfunction of Iraqi society far more than the arrival of democracy is going to fix it. When an American or British person looks and salutes at their flag, do you see the warm glow of pride in their eyes? The Iraqi invasion just made sure that Iraqis won’t feel that glow for the next 100 years.

Was it worth it? I don’t know. I am too small person with too limited resources to decide whether Saddam Hussein was keeping WMDs or not. But I would have liked to see this considered. I would have liked at least one from the trove of political pundits on either side to acknowledge this.

And this is not just a problem with any one nation or any single person. We all underestimate, or completely forget, the need of other person to feel good about themselves. It’s like we have no awareness of ever not feeling that need, so it has become background veil of our thoughts not registering in our consciousness. And we have have no sensation of other person feeling that need, so we discount it while dealing with them.

If we paid attention to this, we would realize that we not only need good things to happen to us, but we need them to happen in such a way that they make us feel good about ourselves.

That realization of abstract, unsurfaced, emotions of other person is compassion. Compassion is not giving a dollar to the beggar. But compassion is realizing that the beggar is as entitled to self-esteem as the queen of England.

And next time when you will get multiple calls in your head, that call of pride or call of virtuousness or call of compassion, I hope you answer the call of compassion. Because that is the golden virtue.

Mindful Exercise – II

In my previous post on mindful exercise, I described how I shifted the goal of my exercise from a number of calories or distance to good feeling in the present moment.

Fast forward one more week. I am still doing it. I am still hitting gym on a regular basis. In fact I look forward to it. However as the time passes and as I can see some improvement in my strength/endurance, I am struggling to stick to the original goal. In a way, the focus of making exercise easier on my body is harder on my mind than I thought.

I continuously find myself wanting to increase the speed, set up a speed or distance target, or simply want to push myself a little more. I find criticizing myself when I see an older person running next to me at 6.0 mph while I am cruising at 2.9 mph. I find myself reaching for heavier dumbbells after looking at a huge muscular guy.

It’s hard to ignore the voice in my head that is constantly clamoring to judge myself based on what others are doing. It’s hard to fight against conventional wisdom in the exercise world that if I am not going faster or higher, then I am not “improving”. As if every thing I do somehow must be set up to make it a conflict, a competition, a race, in which I must come out a winner. And unless I am not, and unless there is no net gain on my self esteem, it’s not worth it.

Years and years of social conditioning at work. Our self image needs regular feed of self esteem, so much so that we are willing to abuse ourselves in the present moment for it.

About the good stuff. Definite and steady positive experiences. My body is happier. It’s happier that I am not abusing it. It’s not scared of exercise and there is no subconscious avoidance or resistance to go to the gym. It does not take any discipline to make me go to the gym. And after an hour of exercise, I come out feeling more refreshed , relaxed and more energetic .

There have been some flashes of interesting insight. One time when doing push ups, and just one short of my intended target, I found myself trying to motivate me.

“Show discipline , stick to the target you decided” says a part of me.

“But the target is mindfulness. If I stick to the target of doing XX pushups, the discipline is in continuing further. But if I stick to the target of being mindful, the discipline is in stopping now because the exercise is not feeling good anymore. ” says the other part.

In that moment I realized very strongly that all the targets, the target to lose XX pounds, the target to run X miles in X mins, or the target to be able to do bench press X pounds are arbitrary. There is no inherent value in the targets. They are important because I made them important with my thinking process.

I stopped push ups one short of my intended target. Let me tell you, it takes a lot of discipline to discard your target in favor of mindfulness.

Here are some lessons I learned.

1. It helps to turn off the distractions like television, or music. That helps me focus on the sensations in my body. It may sound boring at first, but if you think about it, the TV is really helping you distract yourself from the discomfort. If there is no discomfort, or better yet, if there were enjoyable feelings to focus on, do you need the TV?

2. It helps to run the instruments like treadmill on manual setting instead of using one of the canned workouts. On treadmill, play more with inclination than speed. Because I think this exercises big muscles in your leg which I found easier to be mindful.

3. If doing weights, slow and deliberate movements using medium weights work best. Weights just heavy enough for you to feel the exercise, but not enough to cause any discomfort.

4. Be mindful of competitive tendency or peer pressure creeping up.

5. Also be mindful of self criticism for not being mindful, in wanting to be competitive or otherwise. Forgive yourself and avoid self abuse even there.

Mindful Exercise

Some days back, I was reading about cortisol, the stress hormone. The article described the effects of Corisol on body. While reading through the symptoms of elevated cortisol in the body, like tension in muscles, I realized that I may be experiencing some of those symptoms. According to the article, the chronic elevation of cortisol was not good.

I often go the the gym and when I go, I have some set goal, like I am going to run x miles in y minutes. On some days I come out feeling really good and refreshed. On some days I come out feeling more tense and stressed. The article had mentioned that sometimes streneous exercise increases cortisol in the body. I bet that was happening to me.

I decided to set a new goal, not to run a particular distance in particular time, or to life certain weight, or to burn certain number of calories. I was going to target reduction in cortisol. I was going to target that relaxed and energized feeling as a goal itself. Only restriction I would put on myself was that I would stay at the gym for an hour and I had to keep moving even if it meant gentle movement.

First thing I had to do was to be more aware of my body. I had to pay close attention on what feels good in the moment. The moment I noticed the wave of stressed feeling,  I would turn down the speed, or turn down the resistance level, or reduce the amount of weights.

As I focused, indeed I started relishing in that good feeling. There was often a wave of good feeling  when I pushed the weights.  Or liberating feeling when my legs automatically started to run fast at times. I found that making big muscles exercise was often more relaxing.

Result – In last few weeks, there were times I ran/walked only three and half miles in an hour. There were times when I lifted light weights. There were times I spent good amount of time stretching. There were few times when I worked out really hard because I had lot of energy. So all those goals were all over the place.

But my gym attendance record has phenomenally improved. I am making almost all seven days to the gym, unlike three or four days in the past. Most definitely I burned more calories or made more movements than I would if I were targeting calories or distance. My muscles remember the good feeling and as the evening nears, I look forward to making it to the gym. Exercise has become a great  de-stressing and unwinding activity for me. The restriction of making myself spend one hour there does not feel like a restriction at all.

Looks like paying attention to what the body is telling you pays off.


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