Friday, October 28, 2011

Brain Teaser

Suppose you have 4 cards - each will have one side with an alphabet and another with a number.

The side of the 4 cards shown to you are:

A; C; 3; and 6

There is a rule. If a card has a vowel on one end, then it has an even number on the other side.

Question : Which card(s) must you open to prove the above rule is true? I need to limit it to the minimum number of cards to open.




The same question can be re-framed as follows:

Suppose there are 4 persons sitting in a bar.

One is drinking beer; Another Pepsi; the 3rd fella is aged 16; and the 4th is aged 25

There is a rule. Only those aged 25 and above can drink beer.

Question: Who should you check to prove the above rule is true? Similarly, to limit to the minimum number of persons.

Answer: This should be easy - The one drinking beer (A) and the 3rd fella who is aged 16 (3).




What is the morale of the story? This game is designed to prove that our human brain is more sophisticated when it comes to people and less so with abstract concepts such as numbers and letters.

So next time when you are stuck. You just need to re-frame the question. Using analogy and story will help.

Wednesday, October 26, 2011

About Cardboard Boxes


One of the lasting impressions which I have of USA was that it was big on recycling. Cardboard boxes were used, where possible, and in so many varied ways, not limited to the ones detailed below.

Cardboard Boxes in lieu of Plastic Bags

In our weekend grocery shopping which we would always do at Aldi, 2348 Ardmore Blvd, Pittsburgh, PA 15221, our groceries would come in boxes. Not that we bought the entire box of goods, rather it was the way of living of the locals - to reduce the use of the environmental scourge - the lowly plastic bags. In a sense, it fit in nicely into the lifestyle of the locals as they would be driving around to buy groceries and the cardboard boxes would go into the car boot. However, it would seem that much as the locals loved the environment, they loved their gas guzzlers more. Probably, it was a symbol of freedom to travel around that the Americans hold close to the heart.

Besides Aldi, there were also other grocery stores such as Grand Eagle which we would drop by when we went to the campus, Shop 'n Save and of course, the ubiquitious Walmart. Shop 'n Save made an impression on me as it introduced me to the key fob rewards card, where we would produce at our purchase and earned reward points. With driving a vehicle their way of life, a key fob attached to the car key was simply brilliant. For smaller purchases, the plastic bags were still dispensed.

Cardboard Boxes as Lego Pieces and also Furniture

It could have been the environment which promoted creativity and innovation. My two boys quickly found new uses for the cardboard boxes. These cardboard boxes became their life-sized Lego pieces. They would arrange the boxes to make different modes of transportation - on air, land and sea - and play pretend.

Towards the end of our stay, these boxes also found new uses as our makeshift furniture. It was the time whereby we had sold off most pieces of our furniture via the online garage sale.

And if you could just think harder and add on to the above list of uses of cardboard boxes.

Saturday, October 15, 2011

Common Sense in Decision Making

When hunting for a book on probability and statistics a few nights ago, I stumbled onto a book on Combinatorics bought in 1994 and my honours year thesis.

Combinatorics is a branch in Mathematics that study about relationship. An example will be in a room, there are 3 people - A, B, C. A relationship is defined by A knows B. What is the maximum number of relationships? One could draw 3 nodes representing A, B and C; and lines (also known as edges) connecting the nodes to represent a relationship. The maximum number of lines is 3. Try drawing!

In a very simple way, combinatorics is about counting the different combinations. And when we look about relationships, they are highly complex and complicated matters. So even in the era of supercomputers that we are living in, these computers are not that "super". They have their limitations in counting - recall the time, when your computer "hangs"?

Here in, enter the white knight - "heuristics". Heuristics may look like a big word but essentially, it means common sense.

An example will be in the case of an MRT coin changing machine. Suppose there are only 3 coin denominations - 10 cents, 30 cents and 40 cents. What is the minimum number of coins to disburse for the notes that a customer may slot into the machine? The heuristics way will be to disburse the highest value coin first. E.g. $1 note = 40 cents + 40 cents + 10 cents + 10 cents; or four coins.

Most of the time, the heuristics way will give the correct answer, but not all the time. E.g. $3 based on the heuristics way will disburse a total of nine coins - seven 40 cents (i.e. $2.80) and two 10 cents (i.e. $0.20). However, the minimum number is eight - six 40 cents (i.e. $2.40) and two 30 cents (i.e. $0.60).

Every day, people are inundated with decisions, big and small. Heuristics are one of the many ways that people arrive at their choice. It is not only an area of Mathematics but also of cognitive psychology. Hence, heuristics have been researched to understand the decision making process.

Heuristics serve as a framework in which satisfactory decisions are made quickly and with ease (Shah & Oppenheimer, 2008). Many types of heuristics have been developed to explain the decision making process; essentially, individuals work to reduce the effort they need to expend in making decisions and heuristics offer individuals a general guide to follow, thereby reducing the effort they must disburse. Together, heuristics and factors influencing decision making are a significant aspect of critical thinking (West, Toplak, & Stanovich, 2008). There is some indication that this can be taught, which benefits those learning how to make appropriate and the best decisions in various situations (Nokes &Hacker, 2007).

Several factors influence decision making. These factors, including past experience (Juliusson, Karlsson, & Gӓrling, 2005), cognitive biases (Stanovich & West, 2008), age and individual differences (Bruin, Parker, & Fischoff, 2007), belief in personal relevance (Acevedo, & Krueger, 2004), and an escalation of commitment, influence what choices people make. Understanding the factors that influence decision making process is important to understanding what decisions are made. That is, the factors that influence the process may impact the outcomes.

See Mathematics is alive and is everywhere :)

Tuesday, October 11, 2011

No School in Pittsburgh

This series of blogposts is meant to document the Lim's family's memory of the time we spent in Pittsburgh. In this blogpost, I asked my boys of the things that etched in their memory.

The boys were in unison on "no school in Pittsburgh". I supposed for me, it was "no work in Pittsburgh". Hmm, so what did we do there?

The Elite Fly Swat

My elder boy remembered the time when we became the elite fly swat team. We were staying at a rental house at Wellesley Road near Highland Park. It was the lodging sourced by my hubby who arrived at Pittsburgh two months or so earlier. During that time, he had also bought a second-hand car, Chervolet 3.0-litre, silver salon.

A house near our rented place at Wellesley Road


We arrived in Pittsburgh in around May/June of the year. It was the sweltering summer. The curosity act on the part of my elder boy who swung open the back door a tad too long created the perfect opportunity for the gigantic summer fly into the house. The unwelcomed guest was buzzing around my head ever so often.

Armed with a folded newspaper, P and I sat in the middle of the living room and waited patiently to strike at the fly. Alas, the fly while big and dense, was swift. After a few unsuccessful attempts, I decided to close the partition door that would subdivide the living room into two. It would reduce the area which the fly could maneuvor. And voila, the fly was squashed.

This was my first and most unforgetable job as a stay-at-home mother. In a sense, count P in as well as this incident was on the top of his mind.


The Little Snow Man

My younger boy, R was barely two when he was in Pittsburgh. Understandably, his memory was hazy and became more concrete towards the latter part of our stay. He remembered our first snow man.

For the uninitiated, the first day of snow was not suitable to make snow man. It took a few days before the snow became more compact and dough-like. This was the snow that one could play with.

Winter in Pittsburgh

We made our little snow ball by cupping two snow balls - the big one as the body and the small one was the head. The eyes were made of fallen black seeds and the twigs formed the nose and hands. Before all things eco became trendy, we were already embracing it. I supposed you could say that we were trendsetters.

Oh yes, another thing about snow which I learnt was salt could melt ice. I would see my landlord dusting salt on sidwalks. There is the logic. The salt works by lowering the melting or freezing point of water. The effect is termed 'freezing point depression'. So add salt with water to snow, it will become more difficult for the snow to re-freeze with salt. That's textbook science coming alive for us.

Learning without School

On the whole, while there was no school or work in Pittsburgh, we were still learning as long as we opened our eyes, our ears and most importantly our minds. At times, I would be reading my hubby's postgraduate notes with thoughts racing through my mind. There were many others who might have gone through university to learn only to forget after the university. To them, the degree is the end. But learning should be a life journey.

The things that I learnt in Pittsburgh are more precious than what I have learnt in my former school years. It is not about knowing more things but about being inquisitive. Does that mean I will be rich? No in terms of material wealth, but a resounding yes, in terms of happiness and yes, living my life, my way.

Sunday, October 9, 2011

Different tools to manage the economy

Prof Lim Chin was my favorite lecturer at NUS. He was the one who introduced my hubby and I to micro-economics and then macro-economics. He suggested us to read The Economist, talking about which we have been a faithful subscriber since then (close to a decade and counting).

I have utmost respect for this man and his views about economy especially macroeconomic issues. Salute.

Enjoy his article recently published in The Straits Times.

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Different tools to manage the economy By Lim Chin

Although they are both large economies, the United States puts a lot of emphasis on interest rates while China targets the exchange rate in managing the economy and reining in inflation. What is the difference and why?

ECONOMIC growth and controlling inflation are two of the most important targets of monetary policy. The first aims to create jobs and the latter to control prices.

There are different ways to achieve these goals. The US uses the interest rate while China focuses on its exchange rate.

A country may aim to target an interest rate for its currency. It cannot do so directly, but only indirectly, by buying or selling funds in the market. For example, the Federal Reserve - the US central bank - regularly buys or sells short-term government bonds on the open market. This injects or withdraws money from circulation, affecting the short-term interest rate and, thereby, the other rates.

Interest rate targeting is based on the idea that the private sector, and not the government, is best at allocating funds for spending.

In a recession, the Fed aims for a lower rate. This makes it cheaper for private sector companies to raise or borrow money for their expenditure. This raises aggregate demand. But in times of inflation, the central bank works towards a higher interest rate to cool down the demand.

There are, however, circumstances where interest rate targeting may not work. For instance, in the current zero-rate environment, the Fed cannot push the interest rate down any further.

But in normal times, interest rate targeting is effective in curbing inflation or unemployment.

If inflation and recession occur at the same time, as they did in the 1970s, the Fed has to make a judgment call as to which is more important to tackle.

The ultimate aims of China's efforts - increasing growth and reining in inflation - are not that dissimilar to those of the US.

But the institutions that can support its market are still underdeveloped in China and its average living standard is still a fraction of that of advanced economies.

To catch up, its priority is fast growth. So it sees using its exchange rate to drive up its manufacturing exports as the best strategy for now, even though this may lead to unbalanced growth.

Such a strategy has many advantages for an emerging economy. First, it feeds on the large global consumption market rather than the smaller domestic market. Secondly, it attracts foreign investment and technology, and the global market network of multinational corporations.

Competing in global markets also subjects companies to stringent market discipline, thus improving domestic production efficiency.

Over the past few decades, this strategy has taken Japan, South Korea, Taiwan, Hong Kong and Singapore from poverty to First World standards of living.

The strategy, together with other state-directed investment policies, has also produced spectacular results for China. It is now the second-largest economy in the world. It manufactures a large array of goods at low prices.

The strategy has also lifted the national income of its trading partners that produce commodities and resources, and it has amassed nearly US$3 trillion (S$3.6 trillion) of foreign reserves that can help its own domestic development and be lent to debt-ridden advanced economies.

But these achievements come with several problems: unbalanced growth between the manufacturing and service sectors, income inequality between the coastal urban and rural areas and, on the global stage, huge trade imbalances between China and the US. These are acute problems that raise domestic and international political tension, and have been acknowledged as urgent challenges to be tackled in China's latest five-year plan.

Another serious consequence of the strategy is inflation. Keeping the exchange rate low requires the constant purchase of foreign exchange using newly created money, leading to loss of control of its money supply and fuelling housing bubbles and inflation, problems that further increase social tension.

Several measures have been put in place to soak up the money supply. These include foreign capital control, purchase of foreign assets, raising the amount that commercial banks must hold in reserve, and sales of government bonds.

But such policies are costly and only partially effective in taming inflation and asset bubbles. China may have to allow its exchange rate to move upwards sooner rather than later to deal with inflation.

In the long term, when China approaches advanced economy status and has developed market-supporting institutions, including finance markets, it will not need to pursue the unbalanced growth path it is on now.

Instead, it is likely to engage in interest rate targeting and allow its currency to float as the advanced economies of the US and Japan do now.

The writer is a professor at the NUS Business School.
Adapted from an article on the ST, 28 July 2011

Wednesday, October 5, 2011

Chinese Food in Pittsburgh

I missed Chinese food when I was in Pittsburgh. So did my family. There was however a dearth of good Chinese food that catered to our Singaporean tastebuds, served at reasonable price at Pittsburgh.

We tried a few Chinese restaurants. Among the few, I could now remember Lulu's Noodles and Orient Express. Both were value-for-money restaurants which catered to the campus crowd. There was also a Golden Palace Restaurant which was a slightly higher-end one but food being a highly localized product did not appeal to us well. The Chinese food there was somewhere in between Americanized and greasy which locals associated with authentic Chinese food. Consequently, I became the go-to person when my family craved for a taste of home.

That Fuzzy and Warm Feeling

While the Chinese food may not be the main cast when we visited the Chinese restaurants in Pittsburgh, there was a certain warmness in the atmosphere. It might be the loud greetings that one received upon entering the restaurant. It might be the similarities in look that we shared. Then there was a certain feel to the restaurant which drew me in. I felt that I was well taken care of.

It probably had to do with the way the restaurant was laid out which was influenced by the owners. I inferred that the owners were to be some hardworking Chinese migrant family eking out a decent living. The kitchen was set in the background but yet not totally shield from the prying eyes of the diners. This allowed the owners to multi-task - tending to food preparation in the kitchen and yet able to see needs of the diners. This included the times when diners asked for replenishment in certain food served on the stainless metal containers in the buffet section.

Deja Vu at Da Chang Jin in Singapore

Recently, I relived that experience when I dined at the two Da Chang Jin Restaurants in Geylang - one was touting northeastern Chinese food, the other Korean BBQ buffet. While the food was different, the feeling was distinctively the same.

Like in Pittsburgh, the servers were loud. The food was also a tad greasy for our palate. The arrangement of the kitchen and dining areas were strikingly similar as if the owners knew each other's mind. One glance at the place, you knew it was not slick, neat or polished as the upmarket restaurants. But somehow, you also knew that the owners would take care of your dining needs to their best of their abilities.

Unlike Pittsburgh however, I felt that I was a foreigner when I was in the restaurants. The main cliente appeared not to be Singaporean Chinese but mainland Chinese. Notwithstanding, I still had that warm and fuzzy feeling that I was dining in good company. Maybe, this time round, I felt that I was transported back to a Chinese restaurant in Pittsburgh.

Sunday, October 2, 2011

Mental Sum


Question:

There are a total of 150 coins in 14 piggy banks. If each piggy bank contains a different number of coins, what is the largest number of coins that can be found in one of the piggy banks.


========================

My boy tossed this question to his daddy and his mommy during a car ride last weekend. We solved it mentally within 2 minutes. You can do it too, the key is practice.

Of course, there was trick invented by a Math wizard many, many years ago when he was just 5 years old or so. We taught our boys when they were around that age too.

Answer
Container 1 holds 1 coin;
Container 2 holds 2 coins;
Container 3 holds 3 coins;
...
Container 13 holds 13 coins;
Container 14 holds ??? coins


What is the sum of

1 + 2 + 3 + ... + 13 ?
Flip it the other way round,

13 + 12 + 11 + ... + 1
====================================================
14 + 14 + 14 + ... + 14

So the sum is 13*14/2 or 13*7 = 91
So ??? = 150-91 = 59 (Ans)