Missing dollar riddle

I was asked the following question last thursday:

You want to buy a T-shirt that costs RM97. You have no money.

You borrow RM50 each from your brother and your sister and with your current RM100, you purchase said T-shirt.
You hold in your hands the balance (RM3). You then decide to return RM1 to your brother, RM1 to your sister, and keep the remainder.

Now that each of them has RM1 back, the total owed is RM98. If you have RM1, what happened to the remaining RM1?

This riddle illustrates problems of confusion and misdirection can foil a person's clear understanding of the problem.

The original problem is as follows:

Three guests check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realizes the bill should only be $25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn't know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 for himself.
Now that each of the guests has been given $1 back, each has paid $9, bringing the total paid to $27. The bellhop has $2. If the guests originally handed over $30, what happened to the remaining $1?

I shall attempt to solve the original question.

Explanation 1:

The initial payment of $30 is accounted for as the clerk takes $25, the bellhop takes $2, and the guests get a $3 refund. It adds up. After the refund has been applied, we only have to account for a payment of $27. Again, the clerk keeps $25 and the bellhop gets $2. This also adds up.
There is no reason to add the $2 and $27 – the $2 is contained within the $27 already. Thus the addition is meaningless. Instead the $2 should be subtracted from the $27 to get the revised bill of $25.
This becomes clearer when the initial and net payments are written as simple equations. The first equation shows what happened to the initial payment of $30:

$30 (initial payment) = $25 (to clerk) + $2 (to bellhop) + $3 (refund)

The second equation shows the net payment after the refund is applied (subtracted from both sides):

$27 (net payment) = $25 (to clerk) + $2 (to bellhop)

Both equations make sense, with equal totals on either side of the equal sign. The correct way to get the bellhop's $2 and the guests $27 on the same side of the equal sign ("The bellhop has $2, and the guests paid $27, how does that add up?") is to subtract, not add:

           $27 (final payment) - $2 (to bellhop) = $25 (to clerk)

Explanation 2(or the TL;DR version):

The question attempts to confuse you by adding up loaned money. Simply put, the $2 is contained within the $27, and should not be added together.

Why?
An analogous situation would be adding 99 empty pails and 1 full pail of water. The two quantities are distinct from each other and it is meaningless to call the total "100 full pails of water" nor "100 empty pails of water".


The wikipedia entry elaborates further:

Misdirection

The "paradox" cleverly sets its room rates so that when we add the two terms $27 and $2, we nearly get $30. If not for this "near-miss", we would be more inclined to ask if those two terms have to add up to $30 when we break down the situation this way (and to realize that they do not).
With different prices, the illusion would vanish. Say the clerk initially accepted $30 but then learned that rooms are only $10 no matter how many people are in them, and sends back a refund of $20 via the bellhop. Again, the bellhop, seeing that $20 doesn't evenly divide, gives each guest $6 (for a total of $18) and keeps the leftover $2 for himself. Therefore each of the three guests paid $4, bringing the total paid to $12; add that to the bellhop's 2 dollars to get a total of $14. So where did the other $16 go?
With this setup it is more clear that the guests' new total amount paid ($12) is only the bellhop's $2 away from the actual room price of $10, not the original room price of $30. The target price to account for is the new $10 bill, not the old $30 one. In the original riddle it is only the "near-miss" with $30 that makes $30 seem like the correct target of the operation.
The riddle involves the phenomenon of 'suspension of disbelief' inherent in storytelling and its power over the human imagination. If one were to make the story a bit more complex and compelling the illusion is almost guaranteed to work in the moment of its telling and can be a good illustration for the explanation of the anomaly, although not a perfect one because there is an explanation. The more points added to the story cause the listener to pause and try to compute what each element may signify.
There are dozens of variations to the riddle.

Have a nice day.

See also:
http://en.wikipedia.org/wiki/Ignoratio_elenchi

Source:
http://en.wikipedia.org/wiki/Missing_dollar_riddle

Humble Bundle 3.0 -Review- Part II

For our next title, we have...

4. Hammerfight

Hammerfight is about 2D battles of flying machines equipped with various slashing, piercing and blunt weaponry.A unique combat system is based on realistic physics simulation, and it ties the movements of the rider to the movements of your mouse. As you wave the mouse, your rider swings his warhammer, smashing the foe into the wall!

Basically, if you don't play this title, you're missing out on a lot. You feel the strikes as though they are real, and landing a powerful blow is immensely satisfying. It is amazing how the developers managed to simulate the mass of the weapon in your hands, and the physics involved is spot on.

 Hands down my favourite out of the bunch, but the others are still really good.

The controls are sharp and intuitive, and when paired with the realistic physics and smashable objects scattered across the levels and the high quality art, produces an explosion of fun of the highest caliber.

Did I mention that there's multiplayer too?


5. And Yet It Moves

And Yet It Moves is a 2D platformer with a twist. It brings the genre to another level by allowing the player to rotate the game world in 90 degree increments. So simple, and yet, so refreshing.

Your objective in each level is merely to reach the goal. There are no enemies to jump on, power-ups to use, or coins to collect. Conflict is created by the fact that your goal is not immediately accessible. A sheer cliff cannot be scaled -- until you spin the world 90 degrees clockwise, that is, creating a nice flat plain to stroll across.

A spin might give you access to new areas but also send loose rock tumbling down on your head to crush you. You may have to spin the world multiple times in order to manipulate a group of bats into scaring off a man-eating lizard. Playing And Yet It Moves, you're constantly discovering new things. There is a lot of trial and error, but regular checkpoints keep frustration levels down.

The challenges scale in difficulty as you progress. This title is a very pleasing and relaxing experience and is definitely worth a try.


And that's all the five titles in Humble Bundle 3.0. Also, you get free access to Minecraft for free until the fourteenth of August 2011. As Minecraft is not, strictly speaking, physics-related, you'll have to go somewhere else for the review.

Steel Storm is also given away for free if you buy the package. Awesome.

I've devoted 2 days of my student life for this review.

TL;DR: GET HUMBLE BUNDLE 3.0 if you're looking for games that are worth your time.

Humble Bundle 3.0 -Game Review-

Many of you might have heard of the new deal in the gaming world - Humble Bundle 3.0.

Humble Bundle 3.0

Video games that support charity

For those of you who don't know, the Humble Bundle releases are exactly what they seem like - a number of great games with a 'pay-what-you-want' basis, all in the name of charity.

You heard me. Support charity through the purchase of this game!

Here's how the buying works: Purchase the Humble Bundle 3.0 at a price of anything(ranging from $0.01 to as much as you like). Then, you choose how your payment will be divided, between the game developers and the charity organisations. 

Of course, head over to the main site for more information(link above).

Now let's talk specifics. What does this release have in store for us? Before that, we would like to answer the question that is lingering in your mind right now: What is a game review doing in a Physics + Life blog?

1. All of the games featured are Physics-based. (or puzzle-based)
2. To satisfy the readers' desire to fiddle around with physics-based games.

Other physics-based games you should check out are: Fantastic Contraption and Trine

Moving on to the actual bundle:
All of the games are not graphic-intensive, so there's no need to buy insurance for your computer. Besides, all of them are aesthetically pleasing, and your eyes will be saved. Also, all of them have remarkable soundtracks, which will not kill your ears. They also contain hours of limitless fun in each of them.
TL;DR: Great value for money, and you can pay how much you like.

Our first game would be Crayon Physics Deluxe.

 

Exactly what it says on the box, Crayon Physics Deluxe is a combination of two of the greatest discoveries of man - crayon and physics. 

This is a near-flawless example of 2D-based physics problem solving. Levels consist of moving a ball to a star to progress, using any means necessary to do so. One accomplishes this feat by drawing a series of lines, circles and boxes (all of which are affected by gravity) to move the ball.

Do not be fooled by the screencaps.

My only gripe is that the resolution could have been a little higher. That aside, it's a very good game, and very fun to play. 

Game 2: Cogs

Limitless Fun.

Cogs is an award-winning puzzle game for the PC, iPhone, iPad, Mac and netbook. Immersed in a steampunk world with stunning visual design, Cogs players build an incredible variety of machines from sliding tiles. With 50 unique levels and three gameplay modes, we've packed in hours of entertaining, addictive fun.

I couldn't have said it better. This game is hard to describe, but rest assured, it is very fun and is definitely worth your money.

Cogs is a puzzle game similar to the mini-games of Bioshock, if you've played that. (Bioshock would require a powerful graphics card) There's different objectives each time, excellent brain exercises.

Game 3: VVVVVV

If you're just looking for casual, relaxing games, you might want to take a step away from this one. Not because it looks old (actually, they did a pretty good job in making the game retro, and it has awesome music too), but this game is HARD. 

As the captain of an interdimensional craft, you crash your ship, lose your crew, and then get lost yourself. To put it right again, you must explore the collapsing VVVVVV dimension, where you move by upending gravity.

 VVVVVV is a 2D platformer where you can’t jump. Instead you flip gravity on its head and fall upwards (by pressing ‘V’ – or space, or Z), then flip it back. The joy comes from plotting your path across ceilings and floors, around spikes, perhaps over moving platforms, to the next screen. VVVVVV is both reminiscent of long-gone Spectrum platformers, and completely its own game.

Checkpoints are everywhere, and an absolute necessity. The whole game is one long difficulty spike. We died 2,000 times in five hours. It requires absolute mastery of your three movement buttons – one pixel out and you’re dead, slipping off the edge of a platform and up into spikes. And then alive immediately afterwards, thanks to the checkpoints. It’s devilish. Inches from success after hours of failure. Even the small mercy of the frequent checkpoints is turned against you in one brilliant puzzle, where you need to be very careful about where you resurrect. One corridor is called ‘the warning’, and is full of them, mocking you.

It can be frustrating, but only because you’re not doing it right – this isn’t the silly end-boss brand of injustice, nor is it an obtuse lateral puzzle. It’s just a game that requires patience and absolute perfection. A typical puzzle will ask you to weave quickly and accurately through spike-choked shafts, flipping between multiple screens, to land on a vanishing platform for just long enough to flip gravity again, and re-thread the same path. All to cross a knee-high barrier you otherwise can’t jump over.

Which sounds maddening, and anyone watching will think you’re using some sort of self-torture device, but there’s a delicate joy hidden in VVVVVV. When you have to navigate four screens without dying, you can only start to practise the second when you’ve learned to zip flawlessly through the first. It’s like safe cracking – you run, you flip, you wait, you flip, you die, you try again. This time you get to the second platform, and when it raises you into the spiked roof, you notice that you can flip and land on the underside instead.

There are enemies of a sort: the word ‘LIES’ coming out of a megaphone, or spinning coins rotating in a corridor shaped like a dollar symbol. Touch those, touch pretty much anything, and you die. The point isn’t re-doing huge sections of the game when you fail. It’s about failing so often that it becomes a Zen experience. You either complete the level, or you find where developer Terry Cavanagh lives and deliver a horse’s head.

The fierce and relentlessly upbeat soundtrack is dripping with personality, a real labour of love. You could say the same about any aspect – the snippets of dialogue between excited or terrified crew members, the puzzle design, the strobing splendour of the world, and even the names of the rooms. It all makes VVVVVV truly special. It’s a beautifully made game with lots of challenge, atmosphere and polish.

You know that the game truly has to be worth your time because of the huge wall of text above.

I will review the other two games in my next post. 

Recap: The games do not require amazing graphic cards, and are still very good games. Get them, and donate to charity!