Puzzle Corner

[daamon]

Inspired by MackemX's "2 choices, you decide" and "Word Association".

An opportunity to pose non-video related challenges in the form of puzzles, riddles, conundrums or anything thought provoking. Also, somewhere to come if you want a break from lazy noobies stupid questions etc. (not that all noobs are stupid and lazy!).

I shall attempt to review the thread every 5 pages (or so) with a view to listing outstanding entries (can't guarantee I'll get them all, but I'll try).

Rules:

Posting
1. Give your puzzle a title so people posting a proposed solution can refer to it.
2. Your puzzle, riddle, conundrum etc. must have an answer that you know. You can't make up any old crap thinking "that'll get 'em".
3. At your discretion, post the solution if it's been dragging on too long.
4. At your discretion, confirm or deny the correctness of a proposed solution.
5. Give clues and answer questions at your discretion.
6. "Thought provoking" posts can't be related to religion or politics.

Responding
1. If you already know the answer, please resist the urge to post it - let others have a chance at it. No-one likes a smart-arse.
2. Quote the title of the puzzle along with your proposed solution.
3. If possible, provide the page the original puzzle appears on (we'll see how this works) - so others can refer to it.
4. Ask for questions and clues if you want to - you may get a response.

I hope this goes as I'd like it to... Enjoy...

[daamon]

"Two equals One"

Note: a^2 means "a squared" or "a multiplied by a".

Here's one to test your algebra and maths...

a = b
a^2 = ab
a^2 - b^2 = ab - b^2
(a+b)(a-b) = b(a-b)
a+b = b
But, a = b from line 1, so...
b+b = b
2b = b
Dividing by b on both sides gives:

2=1 !!!

Given that the algebra is correct (it is), what's the flaw that allows this false result?

[northcat_8]

how long is long enough to wait?

[Devanshu]

"Two equals one"

a+b = b

[daamon]

seems to me that in the following steps you are dividing the first step by (a-b)....

(a+b)(a-b) = b(a-b)

becomes

a+b = b

.....but since a=b from the first statement, this would imply that a-b=0 and division by zero is undefined.

I posted then quickly edited...I didn't know how long was long enough to wait. Most excellent question though

Absolutely spot on. No need to wait if you've figured it out, only if you know the answer already... Unless, of course, you want to be really honourable and leave it for others to figure out anyway and then smile inwardly knowing you worked it out first...

Well done! Glad you liked it. Got one to offer?

[daamon]

"Two equals one"

a+b = b

In terms of algebra, arriving at this point is correct. However, one of the most sacred laws of maths is violated to get there - as northcat_8 so eloquently states...

[northcat_8]

4 questions....

1. how do you get an elephant in to the refrigerator?

2. how do you get a giraffe in to the refrigerator?

3. The lion king was having a meeting of all the jungle animals but to get there you had to cross a crocodile infested river....how do you cross the river?

4. While at the meeting, you notice that one animal is missing...which one?


I know...fairly easy but I like to use it to show my younger students how they intuitively place restrictions on things or make assumptions that could lead them down the wrong path.

I'll post a more paradoxial situation later, I'm teaching (quiz) right now

[edsmith77]

daamon,
your math is correct (that is the mathematical manipulations) up to the step where you introduce the a=b relationship. Now you are introducing a dependent variable into the equations which were already dependent upon the a=b initial statement. It is not possible to solve a single equation with two unknowns. It takes two independent equations to solve this problem.

[daamon]

daamon,
your math is correct (that is the mathematical manipulations) up to the step where you introduce the a=b relationship.

LOL So, fallen even before the first fence? Darn...

Now you are introducing a dependent variable into the equations which were already dependent upon the a=b initial statement. It is not possible to solve a single equation with two unknowns. It takes two independent equations to solve this problem.

Sorry, I should've started it with "Let a=b", but then I suspect even that wouldn't get me off the hook! It's been a long time since I've done pure maths...

[daamon]

I'll post a more paradoxial situation later, I'm teaching (quiz) right now

A paradox for you, and anyone else, to ponder (you've probably seen it...)

"Statements M C Escher might like..."

The statement below is false.
The above statement is true.

[Cobra]

OK, here's a good 'un for you all that won't stress the maths too much.

You have nine matchsticks. Make four triangles, without crossing any matchsticks. You may not snap any to make two or anything stupid, this isn't a trick question.

Good luck!

Cobra

[SLK001]

"Two equals One"

Note: a^2 means "a squared" or "a multiplied by a".

Here's one to test your algebra and maths...

a = b
a^2 = ab
a^2 - b^2 = ab - b^2
(a+b)(a-b) = b(a-b)
a+b = b
But, a = b from line 1, so...
b+b = b
2b = b
Dividing by b on both sides gives:

2=1 !!!

Given that the algebra is correct (it is), what's the flaw that allows this false result?

You divided by zero.

[stiltman]

OK, here's a good 'un for you all that won't stress the maths too much.

You have nine matchsticks. Make four triangles, without crossing any matchsticks. You may not snap any to make two or anything stupid, this isn't a trick question.

Good luck!

Cobra

[Cobra]

I was thinking upside down! You have SIX matches to work with!

Sorry, guys!

Cobra

[stiltman]

I was thinking upside down! You have SIX matches to work with!

Sorry, guys!

Cobra

Think 3D and standing up

[northcat_8]

This square is 8x8 which would yield an area of 64 square units.

By slicing the square into pieces we can re-arrange the parts to form the following rectangle.



With the pieces ordered we obtain a 5x13 rectangle which would yield an area of 65 square units.


Obviously this is not possible...but why not?

[Cobra]

Northcat, that looks altogether too intelligent for me. I'm a biologist, not a mathematician!

stiltman, you got the answer I was looking for.

Cool,

Cobra

[tgpo]

1. how do you get an elephant in to the refrigerator?

Open the door and put him in there

2. how do you get a giraffe in to the refrigerator?

Open the door, take the elephant out and put the giraffe in

3. The lion king was having a meeting of all the jungle animals but to get there you had to cross a crocodile infested river....how do you cross the river?

Swim across, the crocodiles are at the meeting

4. While at the meeting, you notice that one animal is missing...which one?

Giraffe, he's in the fridge

[northcat_8]

Flawless.

It goes better if you are speaking to them so the Q&A is much quicker, but well played in any event TGPO

[SLK001]

The two "triangles" don't enclose entirely the outside X-Y dimensions.

[daamon]

"64 units vs 65 units"

I don't know if this is what SLK001 said, and I'm saying it a different way, but here goes...

It's because in the smaller, purely yellow triangle, the two shorter sides are in the ratio 3:8. In the larger triangle, the yellow triangle combined with the green four-sided shape, the two shorter sides are in the ratio of 5:13.

This means that the smaller triangle cannot be scaled up (3:8 = 5:13.333, 6:16, 9:24) to be the larger triangle. Hence, in fact, the larger "triangle" isn't in fact a triangle - the longest side is "kinked" where the yellow meets the green. Enough to make the extra square unit.

[daamon]

"Left door or Right door"

You've escaped from the evil wizard's castle which is at the centre of a complex maze. You've struggled to find your way through the maze and, close to getting out, you come across two doors - each of which is guarded by a single guard.

Above the guard on the left is a sign that reads "I always lie", and above the other is a sign that reads "I always tell the truth". A sign is in the middle stating that they will allow you just one question to either guard and then you must choose which door to take, and no coming back.

One door leads back to the castle, and the other to freedom.

What question do you ask? And how do you then decide which door to take?

[SLK001]

Ask the guard that you select, "Which door would the other guard tell me to take?"

[tgpo]

I know I've heard the door one before.

The way it's written you could ask the one who tells the truth "Does you door lead outside?" If he says yes, choose his door, if he says no, choose the other door.

You are working late one night and you need to turn the lights on in the vault so you can see. You have to get your work done tonight or else you will be fired. The light switch for the vault is upstairs, while the vault is downstairs, so from the light switch you can not see the vault. The light switch has three switches on it, and you don't know which turns the lights on in the vault. The vault can only be opened twice from the outside before it is locked down for the night and the door is make so that it can not be pinned open. How can you ensure the lights will be on in the vault for you to work?

[jeex]

could jesus microwave a burrito so hot he himself could not eat it?

[SLK001]

Turn switch 1 on for five minutes.
Then, turn switch 1 off, and immediately turn on switch 2, then immediately go downstairs and open the vault. If the light is on, then the light is controled by switch 2. If the light is off, but warm to the touch, then the light is controled by switch 1. If neither of these is true, then close the vault, go back upstairs and throw the vault light switch, switch 3.

Complete your work, close the vault and be damned forever being an evil moneychanger as an occupation!

[tgpo]

@SLK001

Perfect

[northcat_8]

[Ironballs]

First go to the vault and check to see if the light is off.

If the light is off then the other two states of the switch must change the light on.

[sLiMpAuLy]

OK this is prob to easy but here goes...........


3 brothers are staying in a hotel for the night, they all decide to split on the room. When they check in the desk clerk charges them $30 so they all put in $10 each. They go to their room and are relaxing when the hotel manager notices the clerks error, (he should have only charged them $25 not $30) So he sends the bell-hop to the room to refund the $5. On the way up to the room the bell-hop realizes that the 3 men split the cost of the room equally so he decides to give them each $1 and keep the remaining $2 for himself.

So............Each brother, after being refunded $1, has payed $9.
$9 x 3 = $27.............plus the $2 the bell-hop has and your up to $29


My question to you is where is the other dollar?