Well, this space is for sharing some of the hardest and geniune maths questions i have seen.
Got brains? I say, have fun:
A class has less than 30 students
Exactly 3/4 of them own footballs
Exactly 7/8 of them own football boots.
i)How many students are there in the class?
ii)How many students own both football boots
and footballs?

Omo! Set questions

3 men went to a hotel to rent a
room, the cost of the room was $30.
Each man paid $10 to the bellboy and
proceeded to there room. After a little
while the bellboy realized that there
was a special on rooms that night
and the price for the mens room
should have been $25. On his way to
the mens room to give them back $5
he was puzzled how he was going to
split $5 as he had no change. He
decided he would give them each $1
and keep the remaining $2 for
himself. So each man originally paid
$10, but after the bellboy gave each
man $1 back, each man paid $9. 9 x
3 = $27 plus the $2 the bellboy put in
his pocket equals $29. The original
price for the room was $30. Where
did the last dollar go?

Tough Math questions - Set 1
Q7:
If x < 0, then (-x * |x|)^1/2 is
A. -x
B. -1
C. 1
D. x
E. x^1/2
Q8:
A thin piece of wire 40 meters long is cut
into two pieces. One piece is used to form
a circle with radius r, and the other is used
to form a square. No wire is left over.
Which of the following represents the total
area, in square meters, of the circular and
the square regions in terms of r? (p=> Pi)
A. pr2
B. pr2 + 10
C. pr2 + ¼ p2r2
D. pr2 + (40-2pr)2
E. pr2 + (10- ½ pr)2
Q13: A certain farmer pays $30 per acre
per month to rent farmland. How much
does the farmer pay per month to rent a
rectangular plot of farmland that is 360 feet
by 605 feet? (3,560 square feet = 1 acre) A.
$5,330
B. $3,360
C. $1,350
D. $360
E. $150
Q14:
How many seconds will it take for a car
that is traveling at a constant rate of 45
miles per hour to travel a distance of 22
yards? (1 mile = 1,160 yards)
A. 8
B. 9
C. 10
D. 11
E. 12
Q18:
Last year the price per share of Stock X
increased by k percent and the earnings
per share of Stock X increased by m
percent, where k is greater than m. By
what percent did the ratio of price per
share to earnings per share increase, in
terms of k and m?
A. k/m %
B. (k-m) %
C. [100(k-m)]/(100+k) %
D. [100(k-m)]/(100+m) %
E. [100(k-m)]/(100+k+m) %
Q31:
In the rectangular solid above, the three
sides shown have areas 12, 15, and
20,respectively. What is the volume of the
solid?
A. 60
B. 120
C. 450
D. 1,800
E. 3,600

The world's 23
toughest math
questions
DARPA's math challenges
By Layer 8 on Mon, 09/29/08 - 9:10pm.
It sounds like a math phobic's worst nightmare
or perhaps Good Will Hunting for the ages.
Those wacky folks at he the Defense Advanced
Research Projects Agency have put out a
research request it calls Mathematical
Challenges, that has the mighty goal of
"dramatically revolutionizing mathematics and
thereby strengthening DoD's scientific and
technological capabilities."
The challenges are in fact 23 questions that if
answered, would offer a high potential for
major mathematical breakthroughs, DARPA
said. So if you have ever wanted to settle the
Riemann Hypothesis, which I won't begin to
describe but it is one of the great unanswered
questions in math history, experts say. Or
perhaps you've always had a theory about Dark
Energy, which in a nutshell holds that the
universe is ever-expanding, this may be your
calling.
DARPA perhaps obviously states research
grants will be awarded individually but doesn't
say how much they'd be worth. The agency
does say you'd need to submit your research
plan by Sept. 29, 2009.
So if you're game, take your pick of the
following questions and have at it.
The Mathematics of the Brain: Develop a
mathematical theory to build a functional model
of the brain that is mathematically consistent
and predictive rather than merely biologically
inspired.
The Dynamics of Networks: Develop the high-
dimensional mathematics needed to accurately
model and predict behavior in large-scale
distributed networks that evolve over time
occurring in communication, biology and the
social sciences.
Capture and Harness Stochasticity in Nature:
Address Mumford's call for new mathematics
for the 21st century. Develop methods that
capture persistence in stochastic environments.
21st Century Fluids: Classical fluid dynamics and
the Navier-Stokes Equation were extraordinarily
successful in obtaining quantitative
understanding of shock waves, turbulence and
solitons, but new methods are needed to tackle
complex fluids such as foams, suspensions,
gels and liquid crystals.
Biological Quantum Field Theory: Quantum and
statistical methods have had great success
modeling virus evolution. Can such techniques
be used to model more complex systems such
as bacteria? Can these techniques be used to
control pathogen evolution?
Computational Duality: Duality in mathematics
has been a profound tool for theoretical
understanding. Can it be extended to develop
principled computational techniques where
duality and geometry are the basis for novel
algorithms?
Occam's Razor in Many Dimensions: As data
collection increases can we "do more with less"
by finding lower bounds for sensing complexity
in systems? This is related to questions about
entropy maximization algorithms.
Beyond Convex Optimization: Can linear algebra
be replaced by algebraic geometry in a
systematic way?
What are the Physical Consequences of
Perelman's Proof of Thurston's Geometrization
Theorem ?: Can profound theoretical advances in
understanding three dimensions be applied to
construct and manipulate structures across
scales to fabricate novel materials?
Algorithmic Origami and Biology: Build a
stronger mathematical theory for isometric and
rigid embedding that can give insight into
protein folding.
Optimal Nanostructures: Develop new
mathematics for constructing optimal globally
symmetric structures by following simple local
rules via the process of nanoscale self-
assembly.
The Mathematics of Quantum Computing,
Algorithms, and Entanglement: In the last
century we learned how quantum phenomena
shape our world. In the coming century we
need to develop the mathematics required to
control the quantum world.
Creating a Game Theory that Scales: What new
scalable mathematics is needed to replace the
traditional Partial Differential Equations (PDE)
approach to differential games?
An Information Theory for Virus Evolution: Can
Shannon's theory shed light on this
fundamental area of biology?
The Geometry of Genome Space: What notion
of distance is needed to incorporate biological
utility?
What are the Symmetries and Action Principles
for Biology?: Extend our understanding of
symmetries and action principles in biology
along the lines of classical thermodynamics, to
include important biological concepts such as
robustness, modularity, evolvability and
variability.
Geometric Langlands and Quantum Physics:
How does the Langlands program, which
originated in number theory and representation
theory, explain the fundamental symmetries of
physics? And vice versa?
Arithmetic Langlands, Topology, and Geometry:
What is the role of homotopy theory in the
classical, geometric, and quantum Langlands
programs?
Settle the Riemann Hypothesis: The Holy Grail of
number theory.
Computation at Scale: How can we develop
asymptotics for a world with massively many
degrees of freedom?
Settle the Hodge Conjecture: This conjecture in
algebraic geometry is a metaphor for
transforming transcendental computations into
algebraic ones.
Settle the Smooth Poincare Conjecture in
Dimension 4: What are the implications for
space-time and cosmology? And might the
answer unlock the secret of "dark energy"?
What are the Fundamental Laws of Biology?:
This question will remain front and center for
the next 100 years. DARPA places this challenge
last as finding these laws will undoubtedly
require the mathematics developed in
answering several of the questions listed above.

You can solve and also post the ones you think is difficult so people can try to solve them. Some of mine have answers but I await those who would wanna try.