I have a friend who just loves to torture me with these. He has loads, but here are the ones I remember right now:

1) Just imagine, for a second, that the world is a perfect sphere (ie smooth, no bumpy bits to worry about). Imagine a pice of string is wrapped around the equator, and lies on the surface of the earth. For the sake of argument, assume it is exactly 20,000 miles long (which is about right). Now, if you raise the string off the surface, it will have to be longer to meet end-to-end as it then has more distance to cover right? Question: How much longer would the string need to be if you raised it ONE INCH off the surface of the earth, such that it will then meet end-to-end?

Have a gut feel guess to start with, then do the mathematics. Tell me if you are surprised.

2) Same logic in a way (the brain can't think circularly). Imagine a standard pint glass (or any glass or bottle really, in fact try it with one from the kitchen). Now, you have a pice of string that is wrapped around the bottom of the bottle or glass and is exactly long enough to go around the bottle once, and meet end to end (ie the circumference of the bottle and the piece of string are the same length/distance). If you take that piece of string and straighten it - putting one end on the table and stretching it up against the bottle, how far up the bottle or glass would the piece of string go?

First have a mental guess, then try it. Tell me if you are close.

3) You have a glass of water with some ice in. As we know, ice floats and tends to stick up a bit over the water. When the ice melts, does the level of the water water go up or down?

4) There is a boat on a lake. Suddenly, there is an explosion and the boat sinks. Does the level of the lake go up, down, or stay the same?

5) Imagine a model of the universe, with little balls representing the planets. Assume it is perfectly to scale, ie the size of the planets and the distances etc are in perfect scale to the real thing. Assume the sun is represented by a standard size tennis ball. Assuming everything to scale, how far away is the ball representing Pluto from the tennis ball?

Have a gut feel, then do the math (or with this one, just read the answer when I put it below in a couple days).

Feel free to post answers anyway, just SPOILER warning if you don't want to know answers or hints....then don't scroll down!

Good questions :) I reckon I've got them all (except the Pluto one, where I've only a vague idea...)

Go on then Mik. Key with first couple is its fun to compare first gut-feel guess with actual answers. I still love to show the bottle one down the pub - works every time.

Pluto is 55 miles away from the tennis ball!

Yikes - these are to much like real sums for me. I don't think I'd know where to start. :blush:

Go on then Mik. Key with first couple is its fun to compare first gut-feel guess with actual answers. I still love to show the bottle one down the pub - works every time.

Pluto is 55 miles away from the tennis ball!
LOL well I was well out with Pluto! :laugh:

Q1 and 2 I didn't even begin to think gut-feeling. My first instinct was to think "Pi times D". Sorry.

Q3 the water level stays the same and Q4 the water level goes down.

The fun is just comparing gut feel Fee. eg

1) The string is about 6.28 inches longer. Most people guess miles longer (I think I guessed a 1000 miles longer, but try it down the pub. (calc = 2 pie times radius, radius increases by 1 inch, so length of string increases by 2 x 3.14 x 1 inch).

2) Its a visual one, best to try it after guessing how high up the string goes. Usual guess is MUCH lower than the string actually goes up.

3) level stays the same after the ice melts - some logic there, but all about density and volume and why the ice sticks up out the water

4) Lake goes down - think of a big bucket with bricks in it floating in the bath. Stick a hole in the bucket, and water enters the bucket and the level of the bath goes down as the bucket (or duck) sinks. Something to do with density and water displacement again in that if something floats, the water displaced is greater etc etc blah blah (can't remember the logic, but there is some)

5) As said 55 miles. Thing with this one is we are all brought up seing those little models on tv where everything is in sight - reality is a scale model is too large to represent, so they are always way out of scale on tv. Usual gut feel guess is a few feet.

The fun is just comparing gut feel Fee. eg

2) Its a visual one, best to try it after guessing how high up the string goes. Usual guess is MUCH lower than the string actually goes up.

3) level stays the same after the ice melts - some logic there, but all about density and volume and why the ice sticks up out the water


Had a go at no. 2 with the glass in front of me.
On just looking thought it would come to about half way up the glass.
On measuring it was well over the total height of the glass.

No. 3, I actually thought it would go down, thinking that ice had a higher density than water. Bit too much thinking for this time of night:w00t: