Could you pass a Cambridge University interview?

[doodab]

As the only possible solution to let anyone know their hat colour would be that the prisoner at the back can see 2 red hats and thus knows his hat is green

The guy in the middle knows this, so he knows that if the guy behind him is silent and he can see a red hat his hat must be green. So in that case he would say green.

The guy at the front knows this, so he knows his hat isn't red.

[original PM]

ta!

[OwlHoot]

I got q7 wrong - (and many others) but this one puzzled me. ..

I fell down on a couple of the more arithmetic ones, due to stupid slips, but the hats one seemed fairly easy.

If the guy at the back sees two red hats then he can deduce his is green and call that out. So from his silence, the two guys in front of him know that they don't both have red hats.

But that being so, if the middle guy sees the front guy wearing a red hat he knows his own hat must then be green, and _he_ can call out.

So if neither of these guys calls out, the guy at the front can conclude he is not wearing a red hat (as the preceding two cases cover all possibilities of the front two guys with the front one wearing a red hat, namely front/middle = red/red or red/green).

[The Central Scrutinizer]

I'm not smart enough..

Could you pass a Cambridge University interview? - Telegraph


Lost on this question:

Q.8 An unbiased cubic die has numbers 1 to 6 inscribed on each side. On average, how many rolls will you need in order to get a 6?

Well I answered 1 instead of 6 given that the numbers 1 through 6 and inscribed on each side? But no...

Thickos can't even write the question properly.

I got a blue at Oxford



If I would have hit it a bit harder I would definitely have got position on the pink and then potted the black

[vetran]

Imagine the air was water, which would all want to slosh to the back, making the balloon "float" to the front, as the truck lurched forward

but wouldn't inertia effectively make the balloon appear to go backwards? Depends if the air pressure is greater than inertial forces?

[hyperD]

but wouldn't inertia effectively make the balloon appear to go backwards? Depends if the air pressure is greater than inertial forces?

It's counter-intuitive, but I get the gist of this: the helium balloon is trying to abstract away all the mass type interference.

A better example is here:

Einstein: The elevator, the rocket, and gravity: the equivalence principle

[doodab]

but wouldn't inertia effectively make the balloon appear to go backwards? Depends if the air pressure is greater than inertial forces?

The air has more inertia than the balloon

[ASB]

Really?

Yes. The answer I gave was 2/3 - the nominally correct answer. However, it is strictly an infinite series. It will only be 2/3 if both drinkers have the same number of turns.

The pedantic issue I am getting at is it depends upon the definition of negligible, that would normally be defined as having no bearing on the required precision of the result. However since it is "some" the 2/3 and 1/3 cannot be satisfied unless both have had the same number of turns.

Sure, it tends to 2/3 and 1/3 which is how I would have been required to write the answer.

[ASB]

The air has more inertia than the balloon

A practical demonstration

Driving a Car with a Helium Balloon: Physics - YouTube

[NotAllThere]

I got 80%

But then I DID pass a Cambridge interview, back in 1988

I got 100%. But... I did know some of the answers already. (I passed a Cambridge interview in 1987 - and went to Oxford instead).*


* Only one the facts in that sentence is true.