Getting the right answer

Introduction
In doing mathematics homework, many students find in frustrating not able to get the answers provided.

"problems"
Couldn't get the [given] answer!

"solutions"
Look for careless mistakes and redo the workings. Some keep trying and spend more time than necessary. Some give up easily declaring they are bad in it. Some quickly discover their mistakes and happily conclude that they are not so bad.

My views
I like to tell my tuition students don't over worry about getting the right answer ... Why so and what do I suggest? . The answer is actually very uninteresting. The teacher, markers, question setters already knew it, and majority of the students will know it shortly.

More importantly, in doing homework, the goal is not to get the right answer, but to practice and reinforce the knowledge/skills/techniques being taught. The given answer serves to provide a feedback on your efforts. Some possible feedbacks are:
a) answer is correct ==> what you've done is probably right, and thus providing evidence to reinforce the methods that you have used.
b) answer is incorrect ==> what you've done is not right, thus you should check and learn from whatever mistakes you have made, and thus providing evidence to weaken the methods that you have used.

My point is that the above is achieved by doing the problem using a clear method, check for any careless mistake, compare with the given answer, recheck for mistakes if answers are different, make the conclusion and learn the lesson.

That's it for the purpose of education. Unless the number of correct answers affect your official score, then spend slightly more time to get it right for the purpose of gaining marks, if you know your mistake. However, the additional time spent in doing so doesn't benefit much in educational terms.

The problems with the above "solutions" are:

1) Some keep trying and spend more time than necessary. This is a bad habit that will affect efficiency and productivity in the future real world working environment. A person might be over focusing on a particular insignificant issue but overlooked the main objective and goal of his work.

2) Some give up easily declaring they are bad in it. Making mistake, or not getting the correct method the first time doesn't mean one is bad in maths. It just mean one need to admit that he need to put in more efforts and attention in lessons and revising to improve, but not by getting the answer right without bothering the meaning behind the methods used.

3) Some quickly discover their mistakes and happily conclude that they are not so bad. This is dangerous. It is good that they locate their mistakes quickly, but that isn't the end. Locating mistakes is not evidence that they are good, but overlook that making mistakes is evidence that they are weak. They should try to diagnose the reasons for their mistakes, which usually could be caused by weak foundation in something more elementary. Leaving this untouched, such weak foundation in elementary or fundamental knowledge will continue to haunt them in maths, and even in life.

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Singapore HDB sale exercise (III)

Coming soon...
INTRODUCTION
Continuation from my earlier articles, "Singapore HDB sale exercise" and "Singapore HDB sale exercise (II)"

PROBLEMS
A queue of people with heterogeneous needs and desires make people angry. E.g. in the bank, they have a special counter for opening of account, which takes long time, because imagine how angry people behind who just need to do a 2 minutes simple transaction will be. Here, imagine some whose situation is special and find a typically much undesired unit very suitable for them, but now have to queue together with 10240 people while probably 99% of them will not consider the unity they wanted. Yet, unlike in the bank queue, some of these 99% might change their mind halfway and choose this initially unconsidered unit.

SOLUTIONS
Actually, HDB has already split the locations into 3 sectors. Currently, those who do not desire a unit in the matured estate do not need to queue together with so many others. However, it seems even smaller sectors are necessary. ... What's my idea?

MY VIEWS
May be we should suggest to HDB to allow people to indicate more specifically what they wanted. People who are not aiming for Toa Payoh might lose out due to the many applicants who are attracted by the Toa Payoh units. But then again, you might not lose out since your desired unit might still be there as these applicants probably won't consider other locations.

However, in the current situation, it is very likely that someone who has been given an early queue number to choose to change their mind and choose a unit in a previously not being considered estate. This might not end here, when people change mind last minute, they are likely to regret it, and might end up giving up even though sacrificing 2K option fee, or soon they'll be selling and buying again. Both of these I doubt the HDB welcomes.

I am thinking of using a survey to gather information from applicants if they have specific choices in mind already, and where are these units. Since it is not a first come first serve system, HDB can put up the available unit in advance, allow people to make up their mind on what and where they are aiming for. Then, using the survey results, HDB can appropriately categorize people into different but shorter queues. E.g. if someone stated that he is only eyeing for Ang Mo Kio, he doesn't need to queue together with people who are not eyeing for Ang Mo Kio. Also, encourage people to limit their choice by a priority system. E.g. for estate A, those who only interested in this estate will be the first batch, those who have two interested estates will be the 2nd batch, and so on, while those who aim for any estate will be the last batch in all the queues for all these estates.

This reminds me of MOE. HDB should study the Joint Admission Exercise where students apply for their U/JC/Poly and see how they might incorporate this system in selling/distributing their limited available flats.

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Singapore HDB sale exercise (II)

INTRODUCTION
Continuation from my earlier article, "Singapore HDB sale exercise"

PROBLEMS/"PROBLEMS"
SOLUTIONS/"SOLUTIONS"
See the earlier article.

MY VIEWS
Reference to the sentence, "I am not sure if they have any priority system so that it is not a purely by chance system."

I guess the answer is given by the Minister in the report, "Government to proceed with HDB estate upgrading", where

Mr Mah said: "Balloting method is probably the fairest. Administratively the most efficient way to do it. And we have certain criteria. We have certain income ceiling. We have given allocation priority to the first timers. We have given further chances to those who are living near their parents."

On one hand, I am glad to hear that. On the other hand, I then wonder, is the demand really so huge? ... Why do I wonder? Among the criteria,

income ceiling: I guess it is very clear in he application that all the 10000 over applicants satisfy it.
first timers: I believe I am one although I bought an unit, but it was from resale and without taking grant.
living near their parents: I am.

Yet, my number is 7018. I told others my chance is slim, which is theoretically correct, while my brother replied, "No chance at all!!!", which is statistically correct.

Thus, does this imply that there are at least 7017 others who qualify these criteria? If so, I guess they need to introduce more criteria.

I would not contest that the balloting is the fairest, but is fairest HDB's objective? I don't think so according to the existence of the above criteria.

I admit it is administratively very efficient, and tremendously profitable with virtually pure profit of 10000xS$10! However, being so efficient administratively, this huge revenue is questionable. This can easily be doubled a few times by conducting monthly or even fortnightly ballots, which is very feasible, and each time put up just a hundred units will do. Again, I think it is not HDB's objective to generate revenue.

So, what are HDB objectives? I actually did some readings at the HDB site, and my conclusion is HDB is a builder but not a seller. Their objectives are to make available, and probably also to make sufficiently available. They are not so much into distribution, marketing and selling. Thus, I would suggest they seriously setup a division for it, or outsource to some experts to do this, just as they have outsourced the designing for quite some years already.

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Singapore HDB sale exercise

INTRODUCTION
This is about the Bi-monthly sale of 4-room and above flats by the Housing and Development Board (HDB) of Singapore. The recent offer of 278 units attracted 10240 applications @ S$10 non-refundable fee each.

PROBLEMS
Who are these 10240 people who applied? How many of them are serious and ready in buying? How many of them are trying their luck? Just for S$10 and a few minutes to apply online, they get a chance to buy a subsidized unit from HDB. The chance of 278/10240 = 0.02715 is a good chance to them for a S$10 bet, and a very high potential of gaining 50 to 100K in 5 years time.

However, this is a very, very, very slim chance for serious and ready buyers. ... How is it so? For example, if 80% ~ 8000 are trying their luck, using 10000 in place of 10240 for easy calculation, the expected number of applications from these 8000 getting a queue number in the first 2000 is 8000/10000*2000 = 1600. More specifically, on the average, every 4 out of 5 is a trying luck application. Thus, only 278*1/5 ~56 are serious and ready buyers out of the assumed 20% ~ 2000 of them, i.e. for serious buyer, the actual chance is 56/10240 ~ 0.00547 << 0.02715. Also, by assuming a low successful selection rate of 50%, the first 556 in the queue would have selected all the 278 units.

This system leads to these results. Does HDB want this? I am not sure if they have any priority system so that it is not a purely by chance system. (See my follow-up article on this.)

SOLUTIONS
They are reviewing the system now. Hopefully they can start off with a clear goal and objective in mind for changes and new implementations, rather than a problem solving mind set.

MY VIEWS
I only have vague idea about the earlier systems where it is purely first come first serve basis, and when there are many luck-trying people before serious buyers, the latter has to wait many years for their turn. Probably it was with a problem solving approach, that they dissolves the queue periodically so everyone can have some chance to be a first comer for each sale offer. Yet, long queues started forming up before official announcement of sale killed that system. Then, this present system is implemented where everyone who applies in the first week will be randomly given a queue number, and those who apply thereafter will just continue to queue behind. I guess the assumption is that the number of applications is about the number of units being offered. Sadly this isn't the case this time.

I feel that a week time is way too long a period for online application. My speculations is that most, probably 90% of serious and ready buyers would have applied on the first day. As the news spread out to more people, there will be many luck-trying people submitting their applications. Furthermore, there was this news article reporting that almost 9900 applications on Friday. It is supposed to serve as a deterrent telling people that the chance is low. Yes, indeed, many serious and ready buyers might feel so. However, for the luck-trying people, they might have read it as "Yes, the chance seems low, but this low chance or high volume suggested this is a good bet!" Hence, over the weekend and Monday, there are still another additional 250 applications.

Although something similar to the COE system might help to filter away those luck-trying people, it still has its cons and it is unfair to serious buyers. More importantly, this would be a problem solving way unless the expected resulting scenario is what HDB wants.

Thus, the crucial question is, what exactly does HDB want? What are its objectives and goals? Hopefully whatever new policies and sale systems, will not be for the purpose of solving current situation, but will be designed to achieve their objectives and goals.

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1st hand smoke

Introduction
When a cigarette is lighted, smoke started to diffuse into the air. This is 1st hand smoke.

Problems/"problems"
When a lighted cigarette is not being "consumed" by the smoker, it is polluting the surroundings with 1st hand smoke. ...

Solutions/"solutions"
None yet.

My views
Strictly speaking, smokers mainly inhale filtered 1st hand smoke, and then exhale 2nd hand smoke.

1st hand smoke is probably much more toxic and concentrated than 2nd hand smoke that has gone through the filtering of the cigarette bud, the smoker's lungs, and some of them also the smoker's nostrils. Thus, 2nd hand smoke seems a lesser problem than 1st hand smoke.

Can someone design a filter to cap on to the burning end of a cigarette?

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2nd hand smoke

Situation
In Singapore, and probably also in many other countries, more and more places are out of bound for smokers to smoke.

Problems
When smokers can't smoke at static locations, they smoke while walking. Previously, non-smoker like me who hate 2nd hand smoke can choose not to be near places with smokers. Now, how should I react when walking behind a smoker on a path? ...

Solutions
None yet.

My views
A rationale for implementing non-smoking restrictions on many places is because these are public places, such as eating places, bus stops, etc. Another criteria is when the space is small and enclosed where one cannot easily "escape" out, such as in a lift.

A pedestrian path is a public place, but it is not enclosed, and it is in the outdoor where the 2nd hand smoke concentration would be low. Thus, smoking is not banned here by the above reasoning.

However, when I am walking behind someone smoking at similar speed along a relatively narrow path, I feel like I'm trapped in a space with 2nd hand smoke for some non-negligible period. This is similar to being in a lift with someone smoking. However, unlike in a lift, where I can just hold my breath for a couple of seconds till the door open, it is not easy to do that along a walking path. First, it is more difficult to hold my breath when walking. Second, it usually last longer than a couple of seconds.

Thus, the choices are:
(1) Over take the person in front. However, what if the smoker is walking quite fast, or the path is quite narrow, or what if there are a bunch of them in front?
(2) Halt or slow down till a good distance away from the smoker. However, this means I suffer a lost of time. Also, what if there are also another smoker behind me? Furthermore, this is similar to stopping the lift half way to go out while the smoker go ahead first.

Thus, although the space on a path is not small and enclosed, it has almost the same effect if you happens to walk behind or around people smoking while walking.

Should we call for disallowing people to smoke while walking on public paths, especially those that are narrow or with overhead cover.

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Unemployment rate

Introduction
Every country in the world is working towards zero unemployment rate, or 100% employment rate.

"Problems"
High unemployment rate is a problem.

"Solutions"
Ensure everyone are employed.

My views
Is unemployement a problem? ... I don't think so.

Should we achieve zero unemployment rate by discouraging
a) technology advances, which reduce the number of jobs? This is about number of jobs versus productivity.
b) stay at home moms, if these are technically considered as unemployed? The subtle but significant economic values of "stay at home moms" seem to be totally out of all equations in economic growths.
c) outsourcing, which reduce the job opportunities of locals? This is a battle between local people immediate welfare versus the potential growth and long term welfare for the locals.

Should we increase employment rate by
a) creating/keeping unnecessary jobs so that there are more jobs in the market? E.g. employing people to collect tolls along an expressway versus implementing ERP-like systems to automate collections.
b) breaking up a task into many sub-tasks so that many people can be employed for each little sub-task? E.g. Once I was at a neighbor country's government office, there were 4 staff. Two deal with divorce cases, while two deal with registration of marriage registered in a foreign country. Of the former two, one will briefly check that the required documents are ready, while the 2nd one proceed on with the registration.

I believe good economists are aware of all these. Just as good doctors know that fever is not an illness, while majority of the people only focus on lowering down the temperatures by all sort of ways from taking Panadol to putting ice on forehead.

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