This could be too difficult:

You are given an elliptical-shaped land and you are asked to choose n arbitrary points on its boundary. Then you connect each point with every other point using straight lines, forming n(n - 1)/2 connections.

What is the maximum number of pieces of land you will get by choosing 'n' points on the boundary carefully?

Here are some sample answers:
n=1 Pieces=1
n=2 Pieces=2
n=3 Pieces=4
n=4 Pieces=8


The diagram shows the division of land at n=6,

Practice:

Here are some simple mechanics problems for 'practice':

The diagrams are self-explanatory.

In the first problem, find the force required to keep the platform moving at the constant velocity 1m/s.

In the second, assume no slipping at contacts, and find the accn. of the block in red.

In the third, find the velocity of the wedge after the collision. Assume e=.5.

Facebook Hacker Cup

This is one problem which I could not solve during the contest. (Well, I could not solve any problem)...
You have to command an army of Guards and Warriors in a RTS game to beat Sauron.
Each Guard adds '1' second of game-play to your army, it costs 'G' coins.
Each Warrior deals '1' damage for every second of its existence and costs 'W' coins. All Warriors die when the time given by your Guards runs out.

You have 'M' coins.
Give an approximate answer stating how many Warriors will you buy. Write the answer for the following triplets of(G,W,M).

(15,12,123124423423)
(23,43,234234232489)
(34,24,234879)
(432,25,435354)

Guts:

A charge is kept coaxial with a thin ring, which is made of material with resistance 1 ohm/m. Then it is allowed to fall, under the force of gravity.

In the process that follows, what is the maximum value of current that flows through the ring?

Submit the value of this current, correct upto 3 places of decimal.


From now on:
If you get A/C, do not write your answer as a comment.

Lifespan

A thin tube is inserted into a spherical bubble. Find the lifespan of the bubble.


Assume:
1) Length of pipe=1m.
2) Radius of pipe=1cm.
3) Initial radius of bubble=1m.
4) Surface tension of soap water=1 SI units.
5) Viscosity of air=1 SI units.

Repose

We plan to keep the block of mass 'm' stationary wrt. the wedge by accelerating the latter to the left.

This is possible for a significantly wide range of accelerations. Infact, the acceleration can be anywhere between g*tan(A) and g*tan(B). However, a certain value of acceleration, equal to g*tan(C) is of significant interest.

Your task is to report the values of A,B,C; in degrees. Your answer should be 3 comma separated values, correct upto 2 places of decimal.

Note:
Angle of the incline: 60*.
Coeff. of friction b/w wedge and mass: 1.
PS. : we've done a very similar problem before.

Frustum

A unit charge is placed inside a hollow frustum as shown. Let the flux through the curved surface of the frustum be 'F'.

Report the value of F*epsilon0 correct upto 2 places of decimal. Note down the number of WAs before you get accepted.

A New Year Gift:

Introducing a new feature: Check your answer!
To your left, you should see something asking for your answer. This is automated, so it needs a syntax:

sin(A) is good. Sin(a)/SIN(A)/Sin(A) etc are not..
log(A), ln(A), exp(2) are all good. Don't write e^x.
'g' is g. Its not 9.8, unless specified.
In the question field, choose the question title.

For example: the answer to the last question was "both" (quotes for clarity). The title was "A Frozen Lake". Try it. If it does not work (which is probable as I wrote the code), leave a comment.

A Frozen Lake:

A common concern for anyone who visits the Dal Lake and wants some fun is : "Is the ice safe enough?". The expert's answer is, well, the ice is never safe enough.

But here we'll adopt a more scientific approach. It is well known that
snowmobiles and ATV’s need at least 5 inches, and cars and light trucks need at least 12 inches of good clear ice.

Here are some stats of the Dal Lake:
1)Total depth (water+ice) in winters: 20ft.
2)Surface temperature: -16*C.
3)Bottom temperature: +4*C.

Assume the thermal conductivity of ice: 2.18 units, and that of water: .58.

So, is the ice safe for snowmobiling? for driving? for both? for none?

Angle with the horizontal:

A massless rod has a 'mass' glued to it. The position of the mass is 1m from the left end, and 3m form the right end.

This rod-mass combo is placed on the frictionless inclined-planes shown. At equilibrium, it makes an angle 'B' with the horizontal. What is this angle?

PS: What is the number of cuboids in a 'Rubik's Revenge'? (Ignore the internal structure of the toy.)

To see a Rubik's Revenge: See This