Brick

[rookie1ja]

Brick - Back to the Cool Math Games

One brick is one kilogram and half a brick heavy.

What is the weight of one brick?

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Brick - solution

There is an easy equation which can help:

1 brick = 1 kg + 1/2 brick

And so 1 brick is 2 kg heavy.

An old riddle is as follows: One brick is one kilogram and half a brick heavy. What is the weight of one brick (previously: How heavy is one brick)?

(This is a typical elementary math brain teaser.)

[Guest]

Let brick = x

We know that 1 kg is the weight of 1/2 a brick. Therefore the formula would be:

1/2x = 1kg

2 * 1/2x = 1kg * 2

x = 2 kg

[Guest]

I guess this depends on how you read the question. I read (1 brick is 1 kg) and (1 brick is half a brick heavy), not (1 brick is (1kg + half a brick) heavy). It's the difference between me reading "and" as a logical operator and you reading "and" as an arithmetic operator. Under my version, there are two options:

1. The term "brick" is ambiguous. You just said "one brick" weighs* 1 kg, so how can it also weigh 2 kg? If "one brick" is typical of "a brick" then the word problem is invalid:

1 brick = 1/2 brick

1 brick = 1 kg

1 kg = 1/2 * 1 kg

1 kg = 1/2 kg

1 = 1/2

Since 1 does not equal 1/2, 1 brick does not equal 1/2 brick and the problem is invalid.

2. If "one brick" is not typical of "a brick", then the problem changes:

1 [one brick] = 1/2 [a brick]

1 [one brick] = 1 kg

1 kg = 1/2 [a brick]

2 kg = [a brick]

1 [one brick] = 1/2 [a brick]

1 kg = 1/2 * 2 kg

1 kg = 1 kg

1 = 1

Since 1 does equal 1, this version is accurate, "one brick" weighs 1 kg and "a brick" weighs 2 kg. However, the question is not how much "a brick" weighs, but how much "one brick" weighs, so no math is necessary: "one brick" weighs 1 kg, as stated, and the answer is 1 kg, not 2 kg. As I read it, it's a very simple logic problem designed to confuse by seeming more complicated than it is.

Under the other interpretation, your answer of 2 kg is valid, but it's not a logic problem anymore.

* Technically, kg measures mass, not weight. So a valid answer on Earth would either be 2.2 lbs (the weight of 1 kg sitting on the surface of Earth) or 4.4 lbs (2 kg), depending on which interpretation we went with. Since you said "how heavy", not "what is the weight", this may be an inaccurate semantic argument, but is something I came up with under the logic realm.

[Guest]

I think you understand the intent of the problem which is:

1 brick = 1kg + 1/2 brick.

I agree; the wording could have been better but how many time in high school did you take algebra tests and the wording could have been better there? Usually, you have to determine the intent of the problem to get the answer the teacher is looking for. When you indulge in discrete mathematics, you are then further subjected to the intent of the problem.

[Guest]

"how many time in high school did you take algebra tests and the wording could have been better"

Quite true. If I'd figured out the intent before writing the other solutions I probably wouldn't have said anything, but I'd already written the solution to the other interpretation so I figured I'd post it to add ideas--even if they aren't entirely correct.

[Guest]

If "A" brick is synonymous with "ONE" brick, then the weight of X is 2, ... X = 1 + (1/2X)

In the other possible interpretation of the question however, if "A" brick is NOT synonymous with "ONE" brick, then we *could* assume "ONE" brick (X) is a larger brick, and "A" brick (Z) is a smaller brick. In that case, the equation is impossible to derive an answer for because we can't solve for a value for Z... if "A" brick = banana and ONE brick = apple, apple would weigh 1kg plus 1/2 banana, that is straightforward enough, except we have no idea what banana weighs, and not enough data to determine it.

IE X = 1kg + (1/2Z) with no way to determine Z

The problem yields at least the two following solutions, neither of which yields an answer

X = Z + 2

-----

2

or X = 0.5 (Z + 2)

(Rest of previous post edited to remove any evidence of my previous brain fart....)

[Guest]

lol

applying boolean logic here

One brick is one kilogram "AND" half a brick heavy

1brick = (1kilo) X (1/2 brick) [ 'X' for the boolean operator AND ]

=>2 (brick^2)= 1 kilo

=> (brick^2) = 1/2 kilo

=> brick = sqrt(1/2) kilo

One brick is one kilogram "OR" half a brick heavy

1 brick = ( 1kilo ) + ( 1/2 brick) [ '+' for the boolean operator OR ]

=> 1/2 brick = 1 kilo

=> 1 brick = 2 kilos

[Guest]

1 brick=1kg

[Guest]

1 kg = one brick

[Guest]

Hmmmm does this mean the brick has an infinate weight?

Lets make W the weight of the brick

Weight of brick = Weight of brick + (1/2 x weight of brick)

so...

Weight of brick = W + (1/2 x W)

Substitute w for 1kg

Weight of brick = 1 + 0.5

Weight of brick = 1.5

So this changes the equasion to....

Weight of brick = 1.5 + 0.75

Weight of brick = 2.25

and so on......

[Guest]

i think that... since 1 brick=1kg... and half a brick is heavy (that's how i read it), that 1 brick would be too(2) heavy.

...but obviously that's wrong... ah well, was worth a try, hehe

[Guest]

Each brick weighs 1 Kg and half a brick.....now break this brick.....u will get 2 half bricks weighing 1 kg each....so each brick weighs 2 Kg's

[Guest]

Well, if one brick is 1 kilogram and half a brick heavy, how heavy is half brick?

X= weight of the brick.

X= 1 Kg + 1/2X

X-1/2X= 1 Kg

1/2X= 1 Kg

X= 2 Kg.

Prove:

2Kg= 1 Kg + 1/2(2 Kg)

Isn't it clear?

[Guest]

You cant take the 'and' as a logical operator without rearranging the question

lol

applying boolean logic here

One brick is one kilogram "AND" half a brick heavy

1brick = (1kilo) X (1/2 brick) [ 'X' for the boolean operator AND ]

because, "One brick is one kilogram "AND" half a brick heavy"

is NOT "1 brick = (1kilo) X (1/2 brick)"

and its NOT "1 brick = (1kilo) X 1 brick = (1/2 a brick)

it is actually (1 brick = 1 kg) X (1/2 brick) if you take 'and' as logical rather than arithmetic.

because '1/2 brick' is not a proposition, an attempt to take 'and' as a logical (rather than arithmetic) operator falls apart.

[Guest]

Very Heavy.

Says, 1 Brick Is 1 KiloG

Looks like if the cat thinks 1/2 a brick is heavy

Then a WHOLE BRICK MUST BE CRIPPLING.

[Go Ahead-RAIL 'reallittleman'!]

[Guest]

that's a good one. i approve.

i think that... since 1 brick=1kg... and half a brick is heavy (that's how i read it), that 1 brick would be too(2) heavy.

...but obviously that's wrong... ah well, was worth a try, hehe

[Guest]

Brick - Back to the Logic Puzzles

An old riddle is as follows: One brick is one kilogram and half a brick heavy. What is the weight of one brick (previously: How heavy is one brick)?

(This is a typical elementary math brain teaser.)

If the above contains two statements, then it says that 1 brick is 1 kilogram, and that 1/2 brick is heavy.

If half a brick is heavy, a whole brick must be 2x heavy (regardless of it's actual weight).

2x Heavy could mathematically be written as 2heavy (pronounced TOO HEAVY)

On the other hand, if it is ONE statement, then it says that 1 brick equals 1kg + 1/2 a brick

That means, that 1 brick - 1/2 brick equals 1 kg, and therefor 1 brick must weigh twice 1 kg or a total of 2 kg.

Nive trick question

BoilingOil

[Guest]

You have all brought up valid arguments about how the question should be interpreted, and valid answers dependent on the interpretation, but I just want to bring up the point that this (and the other daily brain teasers) should (more than likely) be analyzed using the most basic logic possible... again, all of your answers (based on your interpretation of the question) are or could be accurate, but it occurs to me that these "brain teasers" are not meant to cause philosophical debates... so (as I do), these riddles should be examined using the most basic terms possible... right?

[Guest]

Brick - Back to the Logic Puzzles

An old riddle is as follows: One brick is one kilogram and half a brick heavy. What is the weight of one brick (previously: How heavy is one brick)?

(This is a typical elementary math brain teaser.)

Remember this is a riddle not an algebra problem so you need to interpret it as such. To clarify, exchange "one brick" for "a brick" then a normal brick would weigh 2/3 kg.

This brick weighs 1 kg but it's 1.5x the normal brick weight. 1 kg = 1.5*Normal_Brick

Normal_Brick = 2/3 kg

On the plus side, since a kilogram is a unit of mass not weight the answer is the same on the moon.

[Guest]

but if its one kilo and half of itself then it is 1kg coz if its halfing itself it would be halfing its original weight which is 1kg. right? im starting to confuse myself is anyone even adding anything to htese forums?

[Guest]

...if its one kilo and half of itself then...

This way of phrasing it inspired me to come up with another way of explaining why the answer is 2 kilos. I know why mathematically the algebraic solution works but like our infinite weight suggestion implies, perspective can change ones own truths. I shal try to explain this through a deductive reasoning as opposed to algebraic or Boolean expressions lol.

OK, here goes…now sit down, buckle up and pipe down lol…this is going to be bumpy :-D

One brick is one kilogram and half a brick heavy. What is the weight of one brick?

(a brick weighs 1 kilo and a half a brick) We know the brick weighs a minimum of 1 kilo right? And each half must weigh at least 1/2 kilo, right? So the minimum weight based on the information must be 1.5 kilos. It is impossible to have it any less than that.

But if the brick weighs a minimum, how do we figure out what the maximum is? We can work backwards using an arbitary answer to get some perspective and answer some questions. (Sometimes it helps to know an answer as to be able to ask the right questions even if the answer is wrong)

Take a brick that is 201 kilos. That is 200 + 1 kilo. A half of this brick is 100.5 kilos right? The problems states the weight is 1 kilo + half a brick. In this case half a brick is 100.5 + 1 and equals 101.5 This does not equal our arbitrary weight of 201 . So the brick at this point does not weight 201 for sure. You could try this with any other numbers and quickly you will see that the number seem to make more sense when they get smaller. So let’s try something smaller

Take a brick that is 4 kilos. (even number this time, much smaller). Half of this brick is 2 kilos right? The problems states the weight is 1 kilo + half a brick. In this case 2 + 1 equals 3 (oh so close but not quite) This does not match our entire weight. Aww..so sad. So needless to say we got closer the the numbers matching as they should but the brick does not weigh 4 kilos. Sorry , please play again !!.

Since 4 kilos was close and we know that the brick must weigh at least 1.5 kilos lets go a notch above that and make it 2 and see what happens. Take a brick that is 2 kilos. A half of this brick is 1 kilo right? (hehe see it coming yet?) The problems states the weight is 1 kilo + half a brick. In this case 1 kilos + 1 kilo equals 2 !! This fits our scenario perfectly. OMG DING DING DING DING DING YOU HAVE WON A TRIP TO THE FABULOUS ISLAND OF….. sike hehe.

Ok, guess that is all . I hope you had as much fun reading this as I had writing it. So many colors and textures in life to explore. I hope you all find time for yourselves to do just that.

Live in the NOW.

[Guest]

i like the too (2) heavy answer

but mathematically you guys are all wrong everyone who says 1.5 kilograms needs to relearn algebra

if

1 Brick=1kg+.5Brick

subtract .5 brick from both side

.5Brick=1kg

1Brick=2kg

but the problem asks for the WEIGHT not the MASS so the answer is

F=MA

Weight is a force measured in Newtons

F=2kg*9.81 m/s^2

F=19.62 Newtons

[Guest]

I think you guys are looking into this way too much. When you're trying to solve a riddle, just take the riddle for exactly what it says. Not "if" this and "if" that.

An old riddle is as follows: One brick is one kilogram and half a brick heavy.

What is the weight of one brick?

I know alot of you out there were saying "Well I read it as 1 brick is 1 kilogram and also half a brick". Truth is, an object cannot weight half of itself, so you're obviously reading the riddle wrong.

Others were saying "I read it as 1 brick = 1 kilogram and half a brick IS heavy." ... Again, you're reading it wrong, it clearly has no "IS" in the original between brick and heavy.

So just read the riddle verbatim:

1B = 1Kg + 1/2B

The word "and" does indicate an addition. Its like if I said, I have one apple and 3 oranges. Exactly like saying 1apple+3oranges.

So...

1B = 1Kg + 1/2B

1B - 1/2B = 1Kg

1/2B = 1Kg

B = 1Kg/(1/2)

B = 1Kg*2

B = 2Kg

Voil?

[Guest]

Brick - Back to the Logic Puzzles

An old riddle is as follows: One brick is one kilogram and half a brick heavy. What is the weight of one brick (previously: How heavy is one brick)?

(This is a typical elementary math brain teaser.)

Since it was ambiguously phrased as "one brick is one kilogram" there is no way to know the answer definitively. Your algebra is correct but there is no way to tell if you interpreted the question right. Just be glad the homonymy of the English language gives us all pointless things to argue about. After all, we could be working

[Guest]

This is the solution I originally thought up. It is an extremely extremely strange way to do it:

A brick is one kilogram plus a half a brick. So, we start with a brick is 1 kilo.

But if it is 1 kilo, clearly the weight of the brick must be 1.5 kilos, because the weight is 1 kilo plus half a brick.

Similarly, if the brick weighs 1.5 kilos, it must, by logic, weigh 1.75 kilos, since, after all, half of 1.5 is .75 and a brick is 1 kilo plus half a brick.

But then again, the brick does not weigh 1.75 kilos, it must clearly weigh 1.875 kilos by the same logic.

This series is clearly converging, but to what? If we write it out:

1 + 1/2(1 + 1/2(1 + 1/2(1 + 1/2(.....))))

or the other way

...(1 + 1/2(1 + 1/2(1 + 1/2)))

So we are left with the relation

a[0] = 1

a = 1 + 1/2 * a[i-1]

Anyway, I don't want to do any more calculus, but it is clear this sum converges to 2. I just thought that was a fun way to do it.