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12 Jun 07
Originally posted by Lincoln Six EchoSorry, I was talking about the type I had when I was a child. The kind where the pedals are directly connected to the axle of the front wheel: no chain, and no brakes.
I say, if the string is pulled forward when the pedal is at the bottom of its rotation two things can happen:
If it is a tricycle with back pedal brakes, then the tricycle will not move or will jerk a bit and then stop.
Or the chain does not lock when back pedaled, and tricycle does not move.
So it doesn't move....seems too easy...
12 Jun 07
1 edit
Originally posted by agrysonWhen given the clues about the woman's political views, most people say "it's more likely that she's a feminist banker than just a banker." However, "feminist bankers" is a subset of "bankers", so it's not possible for that to be true. Mathematically speaking, we have:
hmm... that banker question has me stumped.
As for the ice one, actually the level doesn't change at all, the ice is less dense, by about 10% so 10% of the ice cube is actually above the level of the water and once it melts has the same density so you see no change in the level of the water.
That's an example of what I'm looking for...
Any others?
P(B) = probability that the woman is a banker
P(F) = probability that if the woman is a banker she's also a feminist
P(FB) = probability that the woman is a feminist banker
P(FB) = P(B)*P(F)
Taking the ratio, we get:
P(FB) / P(B) = P(B)*P(F) / P(B) = P(F) {-- less than or equal to 1
Therefore, it's not possible for the probability that she's a feminist banker to exceed the probability that's she's a banker.
12 Jun 07
Originally posted by smomofoIf it's a gentle tug, the trike won't move. If it's a solid tug, the trike will move forward.
I don't know how "real life" this is, but I've seen this in Physics classes:
Suppose you have a tricycle and a piece of string is tied to one of the pedals. If the pedal is at the top of it's rotation and the string is pulled forward gently (by someone standing in front of the tricycle), the tricycle rolls forward. But what will happen if the pedal is at the bottom of its rotation and the string is pulled forward?
12 Jun 07
Originally posted by smomofoIt will move to the back. The air in the car will be slightly compressed at the front during the breaking, creating a horizontal density gradient in the car increasing from back to front, causing the balloon to fly backwards.
You are driving along the road in a car with the windows rolled up and a helium balloon floating around, say, in the middle of the car, when you hit the brakes. Which way does the balloon move in the car?
12 Jun 07
Originally posted by smomofoI don't think this is answerable without more details on the kettle design.
Suppose an electric kettle is 70% efficient when used to heat 1 L of water. Does the efficiency of the kettle increase, decrease, or stay the same if it used to heat 1.5 L of water (assume the kettle does not over-flow)?
12 Jun 07
Originally posted by agrysonYou know what? I think I might have been wrong about the balloon in the car. It might have enough momentum to push aside the air, which admittedly won't be very compressed at all (slightly, but not much). I think sonhouse had a thread all about helium balloons...I'll take a look.
That car one is excellent! but I agree that there seems to be a bit missing from the kettle question...
12 Jun 07
Originally posted by agrysonThe Monty Hall.
Next in the series, I'm looking for questions or problems which specifically make your gut tell you one thing, but that when you think about it more you realise you're wrong.
Not a teaser, it needs to be a question that makes you THINK your first gut reaction is right, but actually would be wrong.
Physics based would be preferred, but it must be an everyday kind of thing.
12 Jun 07
1 edit
Monty Hall is great:
You are on a gameshow with three doors. Behind one door is £500. Behind the other two doors is nothing. You pick one, but before opening it, the gameshow contestant shows that another one is empty, then gives you the option to stick or switch. What should you do?
The unwary will say "switch, the other one has 66% chance as opposed to your current 33%" when in actuality, the gameshow contestant hadn't said he was going to reveal one beforehand, and had you picked an empty door, would probably have let you enter. Thus, it is better to stick.
Oh, and as for my riddlechimp one, the obvious answer is option 2 and say anything, but the best answer is option one and say "you will give me the watch" which forces the chimp to give you both prizes.
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12 Jun 07
Originally posted by PBE6It's probably easiest to think of like this: the balloon floats in the air in the car like a ball floating on water. When the car slows, the relatively heavy air "sloshes" toward the front of the car, and the balloon moves to the back of the car.
You know what? I think I might have been wrong about the balloon in the car. It might have enough momentum to push aside the air, which admittedly won't be very compressed at all (slightly, but not much). I think sonhouse had a thread all about helium balloons...I'll take a look.
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12 Jun 07
Originally posted by agrysonI'm pretty sure that all the info needed is there. Perhaps the only assumption you need to make is that if you heat more water, it is because you actually need to. I'm not sure if that made sense. Do you want my explanation of the answer now, or does anyone want to take a stab at it?
That car one is excellent! but I agree that there seems to be a bit missing from the kettle question...