The all new Brain Teaser thread..with knobs on!

[Byatt]

Given the reciprocal function 1/x, rotated around the x-axis to produce a cone of infinite length, determine the amount of paint required to:

a. Paint the surface of the cone (assume the cone has effectively zero thickness, so inside/outside is irrelevant)
b. Fill the cone with paint.

Enough pi to last you a very long time? ;-)

For the mathematically/programming inclined, I recommend the problems at http://projecteuler.net

[Steve B]

how many bits of cheese does it take to fill a carrot-shaped mouse?

[MadduckUK]

there are SO many variables there..

[JK Ferret]

Two men, 10 miles apart on a straight road walk towards each other, one at 3mph, and the other at 2mph. A dog running at 6mph leaves one man and runs until it meets the other. It then runs between the men at 6mph until all three meet. How far does the dog run?

When does the dog leave the man?

Doesn't matter

Phew... managed to cut out the answer without seeing it

Of course it matters when, if the dog leaves the man at 10 miles apart, it'll run a lot farther than it would have at, say, 1 mile apart.

So, assuming the dog leaves at 10 miles apart, then

sM = 0m, vM = 2m/h, a = 0, t = ?
sD = 10m, vD = 6m/h, a = 0, t =?

using s=vt
we get (for D), 10 = 6t, giving t = 5/3

So at t=5/3, M is at S=2*5/3, = 10/3

Waitaminute... it's been too long since I's done maths, I'll have to paper this 'un, that looks completely incorrect

Brb


EDIT: I give up, I has forgotten too much
EDIT2: well, having looked at the answer, I WAY overcomplicated it!

[RoBe]

Given the reciprocal function 1/x, rotated around the x-axis to produce a cone of infinite length, determine the amount of paint required to:

a. Paint the surface of the cone (assume the cone has effectively zero thickness, so inside/outside is irrelevant)
b. Fill the cone with paint.

good old gabriel's horn
don't forget the domain, x> (or equal to) 1

a) infinite
b) pi(1-(1/a)) where a is the upper limit and is greater than 1

here for anyone that doesn't know what i'm on about

[0iD]

Secure Ltd recently showcased a series of three digit combination locks. The only problem is they were slightly defective. No combinations that started or ended in a zero would work, and combinations worked whether they were entered backwards or forwards. Assuming the no 0x0 combo should be tried, how many combinations would a cracker have to try before they were guaranteed to find one that works?


# combos not in form xyx / 2 + # combos in form xyx

= (9*10*9 - 9*10*1) / 2 + 9*10*1 = 450

[0iD]

A factory that produces tables and chairs is equipped with 10 saws, 6 lathes, and 18 sanding machines. It takes a chair 10 minutes on a saw, 5 minutes on a lathe, and 5 minutes of sanding to be completed. It takes a table 5 minutes on a saw, 5 minutes on a lathe, and 20 minutes of sanding to be completed. A chair sells for £10 and a table sells for £20. How many tables and chairs should the factory produce per hour to yield the highest revenue, and what is that revenue?


Solution:

The optimal answer is to make 24 chairs and 48 tables for revenue of $1200 per hour.
To check it will take 24*10 + 48*5 = 480 minutes of saw time. There are 600 minutes available so the saws will be idle 20% of the time.
It will take 24*5 + 48*5 = 360 minutes of lathe time which is exactly what we have.
It will take 24*5 + 48*20 = 1080 minutes of sanding machine time which is exactly what we have.

[0iD]

This weeks is:
A right cylinder, with a diameter congruent to its height is inscribed in a right cone with height 12 units and radius 5 units. If their axes coincide, find the radius of the cylinder. Hint: By inscribed, this means that the cylinder's whole bottom face is touching the cone's bottom face, and the cylinder is touching the cone with the circumference of the top face.


Solution:

Imagine the axis of the cone form a right triangle. This triangle shares the dimensions of the cone, so it is 12 by 5. Imagine a radius that intersects the hypotenuse of the triangle and call it x. Therefore, we get a right triangle with a smaller right triangle inside. Thus, we can set up a proportion: 12/5 = 12-2x/x. After cross multiplying we get 30/11

[finlay666]

Which football team always plays in 2-5-3 (2 defenders, 5 midfielders and 3 forwards) formation?



A table football team

[0iD]

Duncan and Jamie were going to cut the grass on their square lawn. They agreed that each should cut one-half of the area. Duncan went first, and cut a border 2 metres wide all the way around. After doing a few sums, Jamie agreed that exactly one-half had been cut and happily cut the rest. What was the area of the lawn?


Solution:

Area of lawn was 186.51 square metres.