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

Don

I guess I was aware that I was looking for 3 solutions - and I had used Excel to sketch out the function.  I conducted the fine-tuning around one of the solutions using iteration, but then got side-tracked into the alternative method.

The method of using x=w+1/w is indeed very elegant. I wish I could take credit for it - but sadly I was just following the method developed by someone far smarter than me ! I'm not sure whether you tried working through the method for this problem - but it really is quite amazing how things simplify to the final solutions in terms of Cosine 20,140 & 260.  It also brought back memories of manipulating imaginary numbers !

Thanks to you and all the others who have contributed to this thread - and have helped keep the grey matter active(ish)

Regards,

Peter

ps - Don't want to get drawn into the discussion of whether the kids today have it easier....but my own kids certainly know my views !!

AMP SALES

Total sales were 35 of 250Dr and 45 of 300DR

Nice to have a more gentle algebra problem on Christmas Eve!

Thanks to Don in particular for oiling our grey cells this year. I don't know if you were once a teacher Don, but you would have made a great one!

Kind regards, Steve D 

Thank you Steve. Thank you Peter.

Thank you to all who have contributed too, or simply enjoyed watching this thread these past few months.

Merry Xmas, Don

Bacteria in this sample (apologies that this doesn't sound very Christmas like, or even pleasant after the kind words above - it just happens to be the next one on my list that is simple )

Bacteria in this sample increases at the rate of 30% per day. After 6 days the number of bacteria is 7,500.

How many bacteria were in the original sample ?

The original sample held 2,020 bacteria. I divided the 7,500 by 130 (%) and multiplied theresult by 100 (%) to get the number of bacteria on day 5.  Repeat this four times and you arrive at 2,020. To be sure, I went the other way as well: multiply 2,200 by 1.3 ... -> 7,500 on day 6.

Nice try Mulberry, and I can understand your reasoning and you are going in the right direction, but.................

........................your answer isn't correct I'm afraid to say.

BTW, there is a slight typo....your 2,200 should read 2,020, but its only a typo, the 2020 is correct !

Don Atkinson posted:

Bacteria in this sample (apologies that this doesn't sound very Christmas like, or even pleasant after the kind words above - it just happens to be the next one on my list that is simple )

Bacteria in this sample increases at the rate of 30% per day. After 6 days the number of bacteria is 7,500.

How many bacteria were in the original sample ?

Hi Mulberry,

The experiment starts at the beginning of day 1 and finishes......................

Mulberry had the right concept but just needed another day of bacteria growth to account for. So 2020 ÷ 1.3 puts us back to 1554 at the start of the experiment.

Wish I could find a safe-bet savings account with that sort of growth..........in an economy with 0.5% inflation/growth

Last one (this year )

Windows 10 is awesome

Neat one Frank.

And yes, "X" is pretty obvious too.............but what's this "Windows 10" thingamy....

47 deg

Has somebody hijacked Don account and started posing simple trig questions.

These are all GCSE or the old "O"-Level questions Frank. Nothing difficult.

Of course that was just the "Alternate Segment Theorem" as you, like me, obviously recall.

After all, it is still "Xmas" - back to A-Level next week.............

Cheers

Don

Don Atkinson posted:

back to A-Level next week.............

 

Count me out.

Dear Don,

You made me look out the ten circle angle facts. I used to know them off by heart! I had forgotten the alternate segment one!

I was quite good at Maths, and doing the old Cambridge Board for O-level got a “B” grade at fourteen and an “A” at fifteen.

Unfortunately that was the last exam I would take until I enrolled for A-level, Maths [Pure and Applied, not Statistics], Electronics and Physics as a thirty-nine year old. Good A-levels that actually I do not put on my CV because employers hate the thought of employing someone too bright! Without a degree it pays not to seem too bright! With hindsight this attempt to improve myself was a complete waste of my time.

ATB from George

fatcat posted:

Don Atkinson posted:

back to A-Level next week.............

 

Count me out.

Ok Frank, you are excused the triviality of A-Level. We'll move up to First Year university the following week and you can then join in again just to gently massage that lithe brain..........

George Fredrik Fiske posted:

Dear Don,

You made me look out the ten circle angle facts. I used to know them off by heart! I had forgotten the alternate segment one!

I was quite good at Maths, and doing the old Cambridge Board for O-level got a “B” grade at fourteen and an “A” at fifteen.

Unfortunately that was the last exam I would take until I enrolled for A-level, Maths [Pure and Applied, not Statistics], Electronics and Physics as a thirty-nine year old. Good A-levels that actually I do not put on my CV because employers hate the thought of employing someone too bright! Without a degree it pays not to seem too bright! With hindsight this attempt to improve myself was a complete waste of my time.

ATB from George

 

Glad that one brought back old memories George, it's the one that I think many people forget. (Not Frank of course - obviously )

Another that I simply learned from the old O-level syllabus was to derive the Quadratic Equation. Often the last question and money for old rope! The thing was that we got bored so I could already do calculus because we ran out of stuff in the O-level syllabus!

I am not swanking. It was a talent. Also I had an absolute genius for a Maths teacher, so he set me different home work to everyone else. Indeed it was his daft idea for me to tackle O-level Maths at 14 - just for the fun of it! I had to work much harder for a “B” at A-level aged 40!

Indeed I can still remember most of the O-level things, but A-level has gone very rusty!

ATB from George

George Fredrik Fiske posted:

Another that I simply learned from the old O-level syllabus was to derive the Quadratic Equation. Often the last question and money for old rope! The thing was that we got bored so I could already do calculus because we ran out of stuff in the O-level syllabus!

I am not swanking. It was a talent. Also I had an absolute genius for a Maths teacher, so he set me different home work to everyone else. Indeed it was his daft idea for me to tackle O-level Maths at 14 - just for the fun of it! I had to work much harder for a “B” at A-level aged 40!

Indeed I can still remember most of the O-level things, but A-level has gone very rusty!

ATB from George

Enjoy this week....dread next week...

What a challenge!

Happy New Year! George

...and a happy new year to you too, George

Cheers

Don

Ok, much to Frank’s dismay but (hopefully) to the delight of George and a few others…

…. a couple of “O”-Level (or GCSE) probability questions….

A box contains 5 Red discs and 3 Green discs. Two discs are selected at random without replacement. What is the probability that both discs are of the same colour ?

A box contains 5 Red discs and 3 Green discs. A disc is selected at random, its colour noted and the disc replaced in the box. A second disc is selected, again at random.
What is the probability that both discs are of the same colour ?

I roll 3 fair dice. What is the probability that at least one six is rolled ?

No need to do all three, but you can if you so wish........

Ok, much to Frank’s dismay but (hopefully) to the delight of George and a few others…
…. a couple of “O”-Level (or GCSE) probability questions….

Up-dated to make them a bit more “Christmassy”………….

A totally dark warehouse in Salisbury contains five new 300DR power amps and three old-stock 300 (non-DR) power amps. Two amps are selected at random without replacement to help Frank (Fatcat) develop his aspirational active system. What is the probability that both amps are the same ie are either the new DR models or the old non-DR models ?

A totally dark warehouse in Salisbury contains five new 300DR power amps and three old-stock 300 (non-DR) power amps. One amp is selected at random, its type is noted and the amp replaced in the warehouse. A second amp is selected, again at random.
What is the probability that both amps are of the same type ?

Richard’s annual performance review involved Paul S rolling 3 fair dice. Providing at least one six was rolled, Richard was in for a bonus in the form of a complete Statement. What is the probability that Richard is now the proud owner of a complete Statement ?

No need to do all three, but you can if you so wish........

1. 13/28

2. 17/32

3. 1/2