Logic Puzzles

Working out the formula is straight forward enough, but why would the carpet fitter suddenly be able to work this out from the mathematician's statement?

And what sort of famous mathematician takes a few days to work out an 11 plus level question?

Moving = switching on or off.
Not physically moving the switch to another location.

can i assume no light gets to the cellar - i.e. nothing to do with doing it at nigh time?

You can indeed assume that.

It's not a trick question in any way shape or form.

In your cellar there are three light switches in the off position. Each switch controls 1 of 3 light bulbs on the floor above. You may move any of the switches but you may only go upstairs to inspect the bulbs one time. How can you determine the switch for each bulb with one inspection?
I think I've got this one.

Turn on switch no.1 and wait 10 mins. Turn off switch no.1 and turn on switch no.2. Head upstairs, the light that is on is controlled by switch no.2, the light that is off and cold is controlled by switch no.3, the light that is off but still warm is controlled by switch no.1

Might not work with energy saving bulbs or modern LEDs :(

good work bro, got to be right

Winner.

It's deduction. Because the formula exists it must exist for all diameters of room and central column. Therefore you could have a circular room with a 0 diameter column, at which point the chord length is the diameter of a circular carpet,

Could you show your working on how you derive the multiple of pi that you the area from the chord length. I've run out of room on the paper bag that I'm doodling on.

Could you show your working on how you derive the multiple of pi that you the area from the chord length. I've run out of room on the paper bag that I'm doodling on.

Could you show your working on how you derive the multiple of pi that you the area from the chord length. I've run out of room on the paper bag that I'm doodling on.

If the chord (c) is just the diameter of another circle with the same area, you get

A=π r^2 where r=c/2, so
A=π (c/2)^2 = π/4 c^2

Note there's no radius, of either circle, in the result.

The long way is to take the area:

A=π R^2 - π r^2
A=π (R^2 - r^2)

and find a way to relate the two radii to the chord length.
So, draw the donut, with the chord of unknown length c. Then draw a radius length r of the inner circle, meeting the chord in the middle at a right angle, and a radius length R of the outer circle, meeting the end of the chord

You now have a right triangle, with hypotenuse R and other sides r and c/2, so

R^2 = r^2 + (c^2)/4
R^2 - r^2 = (c^2)/4

substitute this into the area equation above to get

A=π (c^2)/4

If the chord (c) is just the diameter of another circle with the same area, you get

A=π r^2 where r=c/2, so
A=π (c/2)^2 = π/4 c^2

Note there's no radius, of either circle, in the result.

Why is the chord the diameter of any circle? That's only true in the case where the chord goes through the centre of the circle.

The rest makes perfect sense. Thanks, I got too hung up with the 2 right-angle triangles formed by bisecting the chord with the radius R i.e., in the circular sector between the chord and circumference.

Ok, an easy one for Friday afternoon:

Two fathers took their sons fishing.

Each man and son caught one fish, but when they returned to camp there were only 3 fish. How could this be?

(None of the fish were eaten, lost, or thrown back.)

Only one son?

Grandfather?

liking the look of Sam_w's answer

Sam's got it. There is a boy, his father and his grandfather. So two fathers both go fishing with their son but in total there are only 3 people.

Why is the chord the diameter of any circle? That's only true in the case where the chord goes through the centre of the circle.

The chord has some length. I can choose to draw a circle with a diameter of that length. Therefore the chord is the diameter of some circle.

It's deduction. Because the formula exists it must exist for all diameters of room and central column. Therefore you could have a circular room with a 0 diameter column, at which point the chord length is the diameter of a circular carpet,

This thread reminds me of the epic Singletrackworld 'Plane on a conveyer belt' thread from back in the day. Many, many lols were had. Seems to have disappeared up the internet now.

Here's the question (no googling now kids):

On a day with absolutely calm wind, a plane is standing on a runway that can move (some sort of band conveyor). The plane moves in one direction, while the conveyor moves in the opposite direction. The conveyor has a control system that tracks the plane speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction). Can the airplane ever take off?

Negged.

The answer depends on the friction of the wheel bearings.

.

An ol' wild west gunslinger wants to show off his skills, he announces it to the town for weeks and when the time comes a crowd gathers to watch. He warms up with some quick draws shooting cans and bottles from 100 feet, the crowd clap and are really enjoying the show he is putting on. He then announces that he will walk upto the targets and place a blindfold on then hang up his hat and finally have a thick sack placed over his head to totally blind him before walking back not 100 feet but 200 feet and shooting a hole in his hat. He makes the walk down to the targets and has the sherrif check the blindfold and then the mayor check the sack, he has no way of seeing so pure blind shooting and skill, for good measure the mayor insists he spins until he is dizzy. He hangs up his hat, turns and walks back stumbling from side to side still dizzy until he is called to stop and then perfectly makes the shot first time firing blindly.

How did he do it?

Hat already has holes.

Boom!

Hat already has holes.

Boom!

Nope, hat is normal.

Damn.