Ruzzle/Riddle Thread

That last puzzle was the first part of a Cambridge STEP Maths paper - the full question took me about 40 minutes to complete. :eek:

Okay just a quick one this time, with a little physics:
Imagine you have a simple pendulum, whose bob is not solid, but is hollow and is filled with water. While the pendulum is oscillating, a small hole in the bottom of the pendulum is opened, so that water leaks out very slowly.
Describe the motion of the pendulum (qualitatively)
 
Intuition would suggest that the pendulum gradually rises higher as it slowly loses water - but that the period of oscillation remains unchanged.
 
Well, possibly pendulum would move the same speed/heigth, because while losing the water (weigth) it loses also the (kinetic) energy contained in the water.
 
Neither of you are right - so I have a small clue. What does the time period of the pendulum depend on?
 
Well, I was right, but based it on a wrong argument. But if the length of the string is the decissive element, then a pendullum on an infinite line could move only one direction, it would never be able to culminate and go back: it would move in a circle, right?
 
T=2*pi*sqrt(L/g)

So therefore the time period remains unchanged. I'm not sure about the amplitude, though.
 
fo3: Your equation is correct, but your conclusion is not. What is L in the equation (given that we are not talking about a point mass)?
 
hm.. well it should be the distance from the point of attachment to the centre of mass of the bob. Or if we count in the rod, to which the bob is attached, then the centre of mass of the entire pendulum. Now if the water is leaking out, the centre of mass moves.. I would assume it moves lower, and therefore the L would increase and the period would get bigger? If I assumed it right.
 
Two girls were counting their underwear. Macy says to Kitty if you give me one piece of your underwear I will have as many pieces as you have...but Kitty says if you give me one piece then I will have double as much as you have.

How many pieces each girl has?


(Skip the discussion of the hygienic aspect of the trade...)
 
Macy has 5, Kitty has 7.

fo3: Almost right. L is indeed the distance from the centre of mass to the point of attachment, so as the water drains out, the period will initially increase. However, at some point, the mass of water will be too small to lower the centre of mass any more, so it will move back to its original position by the time the water has all drained (light string).
 
@geodesic good,

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You have 5 children in the front of you and a basket with 5 apples in it. Every child must get an apple but 1 apple must remain in the basket. Can it be done?

edited: spelling
 
Last edited:
I have an alternative solution,
Give 4 kids an apple each. Take the last kid, jam an apple down his throat and put him in the basket.
:D
 
In a similar vein:
You have 8 beans and 3 cups. How can you divide the beans between the cups so that each cup has an odd number of beans in it?
 
@Dilbert logically correct sollution, but it wouldn't please the mother of the child...

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(8,5,7) = 33
(6,3,4) = 14
(4,1,4) = 0
(7,5,4) =?
 
geodesic said:
In a similar vein:
You have 8 beans and 3 cups. How can you divide the beans between the cups so that each cup has an odd number of beans in it?
Click to expand...


You put 3 in 1st cup, 5 in the second and then you put the first cup with the 3 beans into the third cup?
 
Dear friends,
I'm watching for this thread from its beginning and I very like it and how you work here. This thread proves that we indeed have wonderful folks in our Forum...
Let me add one more piece in your basket. I found it once somewhere and since that I use it in my practice to illustrate the internal preciseness of Math. There is it.
 
To add a little physics here.
How would you measure the coefficient of friction between a rope and a tables surface, if you could only use a horizontal table, a piece of rope and a ruler?
 
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