Brain Teasers ? or 50 Years On........... ?

Hungryhalibut posted:

Don Atkinson posted:

Hungryhalibut posted:

Don Atkinson posted:

On a happier note for all those “Remainers” (like me) who are depressed or disgusted with the way things seem to be going at present…………

Winter is approaching at a small village in Siberia. The soil in the top two metres above the perma-frost will soon refreeze so they need to dig enough graves in the village cemetery in anticipation of the  number of deaths ( I told you this was on a happier note than Brexit, didn’t I ?)

The village population is 1000 and it’s known that each person has a one percent chance of dying during the winter period.

What is the least number of graves they should dig so the probability of having enough is at least ninety percent ?

I'm informed that the answer is 14.

Hi HH.

You are well informed. Tell Henry he is well up to the mark.

I hope his A Level results get him into his University Course of choice.

Cheers, Don

Hi Don

As you've been so kind in your support of our Henry, I thought I'd let you know that he has got A*AA in maths, further maths and economics, and is off to Loughborough to study maths. And all from Warblington School and Havant College, with not a penny spent on private schooling or tutoring. We are really proud of him. 

That is terrific news Nigel. I really wish him well in his studies at Loughborough and hope he enjoys his time there as well. Is it too early to know were he sees himself heading beyond university ?

Despite his secondary education being state-sponsored, you will no doubt have saved up to help him with his fees and accommodation for the next few years My youngest did 7 years at Newcastle/Nottingham studying architecture and although she had a Gap Year Job and various part-time jobs whilst at Uni, she would have had one heck of a debt if we hadn't helped out. She has had a really good time since leaving, working first with George Clark (the Restoration Man) and now as an Associate in a small practice in London.

He seems keen to go into banking or some such - something that will make a lot of money. How he gets that from woolly lefty parents I have no idea, but good on him. The deal we have is that we pay for the accommodation and the boys pay for everything else. With the loan being about £4,000 and the hall fees being about £5,500 there is no way they can survive unsupported, unless they do significant paid employment. But that's another debate for another day. There is doubtless a brain teaser in there somewhere...

If all Morks are Norks and no Norks are Dorks, which of the following is true ?

• No Morks are Dorks
• All Morks are Dorks
• Some Morks are Dorks
• Impossible to tell

The first one. 

Hungryhalibut posted:

The first one. 

I'm putting this one down to you HH rather than Henry, is that ok ?

It's right , of course.

Remember those things called "identities" ?

Sin²β + Cos²β = ??

Cheers, Don

Don Atkinson posted:

Hungryhalibut posted:

The first one. 

I'm putting this one down to you HH rather than Henry, is that ok ?

It's right , of course.

Yes, it was me. I don't think I could answer it in my present state though!

Hungryhalibut posted:

Don Atkinson posted:

Hungryhalibut posted:

The first one. 

I'm putting this one down to you HH rather than Henry, is that ok ?

It's right , of course.

Yes, it was me. I don't think I could answer it in my present state though!

We'll look forward to your next contribution in the "Which wine am I drinking ?" thread......

Using identities and starting with Sin 45; Sin 30; Cos 45 etc can you show how

Sin 15 = ¼[√6 - √2]

Don Atkinson posted:

Hungryhalibut posted:

Don Atkinson posted:

Hungryhalibut posted:

The first one. 

I'm putting this one down to you HH rather than Henry, is that ok ?

It's right , of course.

Yes, it was me. I don't think I could answer it in my present state though!

We'll look forward to your next contribution in the "Which wine am I drinking ?" thread......

If only....

Don Atkinson posted:

Remember those things called "identities" ?

Sin²β + Cos²β = ??

Cheers, Don

Just to ensure this doesn't get swamped and also to avoid ambiguity

(Sinβ)² + (Cosβ)² = ??

It's the same thing as I posted half a dozen posts above. It's meant to be a gentle re-intro to identities 

Don Atkinson posted:

Don Atkinson posted:

Remember those things called "identities" ?

Sin²β + Cos²β = ??

Cheers, Don

Just to ensure this doesn't get swamped and also to avoid ambiguity

(Sinβ)² + (Cosβ)² = ??

It's the same thing as I posted half a dozen posts above. It's meant to be a gentle re-intro to identities 

OK, I know it was a bit easy, Sin²β + Cos²β = 1

Don Atkinson posted:

Using identities and starting with Sin 45; Sin 30; Cos 45 etc can you show how

45Sin 15 = ¼[√6 - √2]

Try starting with the identity for Sin(A - B) = ..............

And recall that Sin 45; Sin 60 etc are nice, easy fractions !!

Hungryhalibut posted:

Don Atkinson posted:

Hungryhalibut posted:

Don Atkinson posted:

Hungryhalibut posted:

The first one. 

I'm putting this one down to you HH rather than Henry, is that ok ?

It's right , of course.

Yes, it was me. I don't think I could answer it in my present state though!

We'll look forward to your next contribution in the "Which wine am I drinking ?" thread......

If only....

Hi Nigel,

I have been in remote areas this past week and only just noticed your accident report in another thread, terrible. I wish you well and trust that you make a full recovery.

I endorse your view that road users should undergo so sort of competence and/or medical review on a regular basis.

To maintain my flight instructor's rating I need a medical every 6 months, a flight test every three years plus a lot of actual flying or a two-day seminar. To maintain my instrument rating I need a further flight test every twelve months. Sometimes it seems like I need a test of some sort or other, every three months ! I have to pay for all these tests.

I think a driving test and medical for road users at the age of 60 would be a good idea, followed by a further test at 70 and then every 5 years to 80 and then every two years to 90, then every year.

But again, I do wish you well and a speedy recovery.

Cheers, Don

Thanks Don, much appreciated. There certainly needs to be some sort of testing, though there is clearly an issue of upset to millions of older people, who also happen to be conservative voters. That's no reason not to do it, but is a huge issue to overcome. 

Hi Don,

sin(A-B) = Sin A Cos B - Sin B Cos A

if A=45 and B =30

sin (45-30) = sin 15 = sin 45 cos 30 - sin 30 cos 45 = √2/2 x √3/2 - 1/2 x √2/2=1/4 x [√6-√2]

Best wishes

Matthew

Well done Matthew.

These sorts of things take me back 50 years or so. We hardly ever knowingly use them in our working lives, although I do use approximations every day based in the Sine Rule and the Cosine Rule and a few other bits of geometry and trigonometry. And i'm sure that many bits of equipment and structures were designed with similar approximations, well before digital computers were around.

A disc of uniform density has a hole cut in it as shown.

Find the centre of mass.

Don

I'm conscious that I haven't tried one of your teasers in a long while - so time to come out of "retirement" !

I'm assuming this is one of your wicked problems that looks very easy - but actually requires a lot of number crunching and with scope for lots of errors. With that caveat I will have a stab at saying the centre of gravity is along the horizontal centre line and located 38.8 mm right of centre.

Regards,

Peter

ps - Many congratulation on your recent press fame.

Hi Peter,

Nice to see you coming out of "retirement" and many thanks for your kind words.

This one looks straightforward and should have been straightforward.

You are spot-on that the centre of mass is on the "x" axis, and is to the right of the "y" axis - symmetry provides that part of the solution, But.....

.... I drew the 200mm dimension wrong, it should have represented the diameter of the orange area which should be a 200mm diameter circle. The hole is 100mm diameter.

Serious apologies !

I think you will find my intended Teaser a lot, lot easier.

I now have the problem of trying to solve [an orange elipse (400 x 200)] - [a white circle (100mm dia)] to see if I get 38.8mm, assuming that's what you have done ?

I'll say "well done" now, because it certainly looks about right.

Buhga the theory,  I worked out the off-set C/G of my NDX this afternoon using a golf ball - in case anyone asks, not gone completely off the rails, yet.  I was setting up position of Vibrapods under a new glass support shelf   ...........   now what was the question again ??? 

...........or we could try two elipses.........400x200 minus 200x100.............

....however, I don't think any of the three options I have now put on the table are too difficult (well, I hope not !)

ps I really wish I hadn't made that draughting error !!!!

Mike-B posted:

Buhga the theory,  I worked out the off-set C/G of my NDX this afternoon using a golf ball - in case anyone asks, not gone completely off the rails, yet.  I was setting up position of Vibrapods under a new glass support shelf   ...........   now what was the question again ??? 

the question keeps changing  .... 

Don

I had actually assumed that the diagram was meant to be a circle within a circle.

I had taken the orange circle as radius = 200mm and the inner circle as radius = 100mm

I then worked out the angle subtended at the centre of the orange circle which formed a segment equal to 1/2 of the remaining area (ie orange circle area - white circle area). Once I had the centre angle, then you can you cosine to find the displacement from the centre. I'm pretty sure this method will work - but it isn't very elegant because the segment area is derived from "Theta" ans "Sin Theta". Messy !

I'll have another go based on your latest dimensions when I get the chance. And will think more about the obvious solution that I must be missing ?

Regards,

Peter

Ok

So I now get the centre of mass to be 20mm to the right of the centre of the orange circle.

This was derived using the sledge-hammer approach. Now to think of the more elegant method........

Regards,

Peter