Brain Teasers at Xmas

Posted by: Don Atkinson on 23 December 2010

Brain Teasers at Xmas

Xmas time - and many of us will be off on holiday or meeting up with friends and family. For those with a bit of time on their hands, I thought I would post a dozen (12 days of Xmas ?) brain teasers to help keep your minds in gear.

All are taken from the Brain Teaser thread from a few years back and credit is given to the original poster where this is other than me. Ken c still posts here, but BAM and Matthew T….??

None of these teasers are “trick” questions, but you will need to read them carefully in order to understand some of them. Discuss at leisure......

I know it’s not as exciting as today’s hi-tech electronic games, but I hope it helps to keep some of you amused over Xmas, and as Ken c would say – “enjoy”

Cheers

Don
Posted on: 19 March 2011 by rodwsmith
I am stuck on someone else's brain teaser. Can anyone tell me the name of the person in this picture? (It's only part of the clue). Or even just if he has something to do with the state of Oregon.

 

I'd be very grateful!!!
Posted on: 19 March 2011 by Don Atkinson

Rod,

The building in the background doesn't look like the State Capitol building in Oregon.

A quick look in Google suggests the Capitol building in Oregon has an octagonal dome.

Hopefully someone else will be more helpful.

Cheers

Don

Posted on: 19 March 2011 by BigH47
Is it the V-POTUS?
Posted on: 20 March 2011 by rodwsmith
Thanks!

I'm sure the building is the Capitol in Washington, and alas I really don't think that is a photograph of Joe Biden, although it does look a little bit like him. The picture seems too familiar somehow.
Posted on: 21 March 2011 by rodwsmith
It's Bob Dole I discovered. Which figures neatly.

Cheers!

Rod
Posted on: 21 March 2011 by Don Atkinson
Glad you got that one sorted Rod.

looks like this is more of a "self-help" thread rather than an "ask Jeaves" thread.

Cheers

Don
Posted on: 21 March 2011 by Don Atkinson
Straight from tonight's University Challenge...........

5 robots assemble 5 machines in 5 minutes.

How long will it take 100 robots to assemble 100 machines ?

Cheers

Don
Posted on: 22 March 2011 by steved

Don,
The intuitive answer is 100 minutes, but of course this is wrong.
It takes 25 "robotminutes" of input to get 5 machines of output, ie 5 "robotminutes" per machine. 100 machines will therefore need 500 "robotminutes". So with 100 robots, you will need 5 minutes.
Steve D

 

Posted on: 22 March 2011 by Don Atkinson
Steve,

Yes, I think most people have that initial thought "100 minutes", but somehow hesitate and then realise the correct answer.

Cheers

Don
Posted on: 24 March 2011 by Don Atkinson

I realise that I never got around to posting the formula for the “goat that is tethered to a post on the perimeter of a circular field radius 1.0, such that it can only eat half the grass”

You will recall that the length of rope (L) can only be found by iteration. My formula is:-

 ArcSin(y) + L^2ArcSin(y/L) – y – pi/2 = 0 

Where y = 0.5L [4 – L^2]^0.5   and all angles are in Radians

Its easy to set up the equation in Excel and do a manual iteration ie trial & error until you find a value for L such that the equation = 0

I started with L = 1. The value of the LHS is < 0 so L is too small

Try L = 1.1  again LHS is < 0 so L is too small

Try L = 1.2 and find that LHS > 0 so L is too large, so revert to L = 1.1

Try L = 1.11 and the LHS is < 0 as is 1.12, 1.13 1.14 and 1.15

      L = 1.16 gives LHS > 0 so L is too large, so revert to L = 1.15

Try L = 1.151 etc etc

I’m sure that Excel has something called “goal-seeker” or some other feature that would do the iteration automatically………..

Hope this is all perfectly clear to everybody………

Cheers

Don  

PS I have had to use ^ to indicate that the subsequent figure is a "power" eg ^2 = square and ^0.5 = sqrt

Posted on: 25 March 2011 by Don Atkinson
Oh ! I thought i'd better post the answer close to the formula so that future users of the "search" or "google" get a meaningful return.

Length of goat rope is 1.1587285

Saves going back a couple of pages.

Cheers

Don
Posted on: 08 June 2011 by Don Atkinson

Resurrected in response to "requests" in another thread.

 

There are a couple of outstanding (*)  teasers on the previous page

 

Cheers

 

Don 

 

(*) Outstanding in the sense "not yet solved"

Posted on: 08 June 2011 by Martin_C

...outstanding from Xmas!!!

 

....blimey seems like only yesterday ....I think we should all get out more.

 

I always liked the teasers where there is a simple way of doing it and not very simple way of doing it. For example:

 in the good old days when there were 96 teams in the football league, all of whom were eligible to play in the league cup. Assuming no replays, how many matches in total were played in the competition.

 

.....I'm embarrased to say that I worked out how many teams would have a bye in the first round!

 

Alternatively there is always the management consultancy entrance exam which starts with Question 1 of 4: How do you get an elephant in a fridge?

 

Martin C

Posted on: 08 June 2011 by Don Atkinson

Martin,

 

I'm guessing your answer was 32 instead of 95

 

Not sure that its always 1 less than the number of teams starting, but it looks that way.

 

Cheers

 

Don

Posted on: 11 June 2011 by Martin_C

Don

 

Yes, my problem was that I got to 95 eventually but by totalling up the games in each round rather than by subtracting one from 96.

 

Incidentally, have you considered a new career setting exam questions for AS level students - I think there are vacancies in the maths and biology departments?

 

Martin

Posted on: 11 June 2011 by Don Atkinson
Originally Posted by Mart

have you considered a new career setting exam questions for AS level students - I think there are vacancies in the maths and biology departments?

 

Ooo! I hope the teasers I posted aren't so badly worded that I might qaulify for setting AS exam questions.

 

Cheers

 

Don