egoistic post

haha. was looking at vjc maths dept website for some other purposes... and to my pleasant surprise. i found a paper that was written by yours truly seven years ago...

it's about non-transitive dice. basically, it's about a set of dice, call them A, B and C, with numbers which are not the usual ones. we have A being more likely to win B, B more likely to win C and (here's the weird thing) C more likely to win A. through some stroke of luck, i managed to find a way to create a set of non-transitive dice, of any size and each dice having any number of faces (strictly speaking, a dice should have 6 faces). with some fanciful presentation, the team managed to get some gold award in some science festival. haha.

oh... i also remembered getting pm lee's (then dpm lee) autograph on a report for e project. e amazing thing was that he knew about our topic by just looking at the title. (not many maths pple know wat are non-transitive dice) i knew he knew cos he asked, "so how many triplets did u come up with?" when the title of the project did not give any hint of the set being a triplet. n u can guess my answer...

haha. this post is so bhb...

guide to solving bohliao puzzles

stayed onboard on monday and my boss was feeling boh liao and got all the officers together for supper. now is uni vacation, so got a lot of young officers who are attached to ship to entertain my boss. somehow, they started asking each other stupid puzzles which seem to make my boss relive his younger days. dunno if it's "i'm a maths guy" or it's "i got a super memory for puzzles". i seem to have heard most of the puzzles and recall the solutions readily.

anyway, while it seems the puzzle require some great ingenuity or wat pple call "think out of the box", it's not difficult if one attempt to use some method. (maybe different pple got different sizes of boxes to think out of) here's a simple tip to solving most maths-related problems.

reduce to a simpler/smaller case.

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example 1. there are 10 boxes, each containing 10 marbles. in 9 boxes, the marble each weighed 1 gram and in one box, the marble each weighed 1.1 gram. we have an electronic weighing machine which can give the exact weight.
aim: in one weighing, find the box with the heavier marbles.

some analysis: obviously weighing everything together will not help and ppl get stuck here. Let's reduce to 2 boxes with 2 marbles each. One has marbles weighing 1 gram each and one has marbles weighing 1.1 grams each.

how many marbles from each box should i choose to weigh? if i take 2 marbles from each box, i'll definitely get the reading 4.2 gram. similarly, if i take 1 marble from each box, the reading will always be 2.1 gram. ie. no conclusion.

now, let's name the boxes B1 and B2. if i take 1 marble from B1 and 2 marble from B2.

if B1 contains the heavier marbles, the reading will be 3.1 gram. if B2 contains the heavier marbles, the reading will be 3.2 gram. there's a different reading for each possibility. that is, we are able to conclude from the reading which box contains the heavier marbles.

hmmm... not v difficult to guess the solution for 10 boxes and 10 marbles right?

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example 2. there are 8 marbles with 1 lighter than the rest. there's a balancing weigh (ie those see-saw type which can tell which marble is heavier).
aim: in two weighing, find the lighter marble.

let's reduce the problem. in one weighing, how can i find a lighter marble?

let's call the scales, left and right. in one weighing, how many possible outcomes can there be? three. (A) the left being heavier, (B) the right being heavier, (C) both just as heavy. hmmmm. so, if i got three marbles with one lighter, i just weigh any one against another. (A) would imply that the right is lighter. (B) imply the left is lighter. (C) would imply the one not weighed is lighter.

it's also clear with only 3 possible outcomes, there's no possible way to find a ligher marble from a pile of 4 marbles with just one weighing.

so, returning to the question, let's say we completed the first weighing. we must conclude that the lighter marble is one in a pile of 3 marbles. So, that means, in our first weighing, we must weigh a pile of 3 against another pile of 3. the rest of the details can be worked out easily.

as a maths guy, i like to generalise the problem. so, in N weighings, it's possible to find a lighter marble from a pile of at most 3^N marbles. So, if some guy ask you to find the lighter marble from a pile of 30 with just 3 weighings, you can tell him, mighty mao say impossible.

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hmmm. so where's the box to think out from?

super boh liao post

any guesses to where's this picture taken? Yes... it's sentosa. more specifically, it's a small island off palawan beach.

and it's claimed that this is the southern most point of continental asia. ie.. if you wanna head south some more. u must jump into the waters and get wet.

then... at work, when i was looking at charts (the naval term for maps), i realised something... then i decided to verify with google earth... and to my astonishment..


the so-called "southern most point of continental asia" is NOT the southern most point!!!!

running

realised that i'm getting fatter... my appetite getting bigger. yesterday was eating and eating at the steamboat with the roosters while mika was talking about her adventure at macritchie..

anyway, been running q a bit lately. running prob the best way to keep fit for a psychomotor-impaired guy like me..

joining the milk run with mika and soka this july. hoping to find pple to go for the mizuno wave run at bedok reservoir in late july.

today found this website, called mapmyrun, which plots down a running and calculate the distance q efficiently. the streaming is much faster than the streetdirectory.com, so actually one can use it to navigate in singapore much faster. not sure how often it's updated though...

below is the regular route which i run usually. 5.68km.

target for the end of the year: 42km standard charter marathon.

genting trip

While mika goes to tioman with her family, me decides to go out with my jc friends to genting. it was a long time since we went overseas together (the last time was to hk after a levels)... anyway.. q difficult to describe and imagine wat we did and how we actually can derive fun from it... basically, was just gambling, eating and chilling out. and 'occasionally' bitching about the 'efficiency' of the place...

moreover, it's q disturbing to realise that genting (e company) in a few years' time will be running the sentosa's integrated resort.

things i hope they'll learn:

1. to have a much more parking slots with a properly managed carpark. and not to allow cars parking out of proper parking lots.

2. to have a nicer reception lobby which does not remind one of a refuge camp (with hundreds of ppl waiting with luggages) or an A&E ward (with queue numbers LED display).

3. to have Kenny Rogers' Chicken to be served with the side dishes and not serve a plate with sides dishes only.

4. to manage a HUGE crowd during public hols.

5. to have an eloquent service, which is able to describe food on the menu (even though the food is not what they can eat).

6. to have a friendlier service. (kaimin wanted to upgrade his genting card to some genting 'green' card. the lady at the counter told him to do so in the casino and sacarstically told him that he has to wear polo t-shirt into the casino... huh? we entered the casino without any shirt/polo t for two days...)

7. to have fastfood served fast. (as pointed out, the elderly at mac's or the handicapped at kfc serve much faster)

hmmmm... but all in all, still enjoyed e trip and it was an excellent break from work.