46 replies to this topic

[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?

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.
Pls visit New Puzzles section to see always fresh brain teasers.

Spoiler for Solution

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.

Spoiler for old wording

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.)

[netwebdave]

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

[fosley]

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.

[netwebdave]

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.

[fosley]

"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.

[JeffR]

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....)

[Cyr|x]

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

[lukegaru]

1 brick=1kg

[thutanyi]

1 kg = one brick

[freeonlinelaughs]

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......