Brain Teasers ? or 50 Years On........... ?
Posted by: Don Atkinson on 02 June 2015
50 Years on…….
50 years ago, I was doing what many 18 year olds are doing this week and over the next few weeks……………….their A-Levels.
Mine were Pure Maths; Applied Maths; Physics and Chemistry. We also had a new subject called The Use of English.
About 10 years ago I started a few “Brain Teaser” threads on this forum. One or two people complained that many of the so-called Brain Teasers were no more than A-Level maths dressed up. That was true of a few teasers, but most were real teasers, especially the ones like “The Ladder” posted by Bam and also the one about the maximum number of 1cm diameter spheres that can be packed into a 10x5x5 cm box.
Any way, never mind Brains or Teasers, I guess one or two other Forumites are also looking back 50 years and would be delighted to tease their brains with calculus, probability, spherical geometry, geometric progressions, Newton’s Laws of Motion ……………………….no ? Then probably best if you drink your weekly 21 units tonight and wake up in the Music Room tomorrow to recover from the nightmare !
First one to follow shortly, and please, please add your own favourites !!
Posted on: 06 November 2015 by fatcat
Originally Posted by Steve J:
Interesting. Things don't change much over the years. When I was a junior doctor starting out in 1979 I worked out my hourly rate. I used to have two evenings off a week and every other weekend off, all other time was spent in the hospital. My hourly rate of pay was less than 20p an hour.
Queue the Monty Python sketch. 
I used to watch St Elsewhere every week and if I remember correctly the doctors had a little cubbyhole with a built in bed.
Wish I could get 20p an hour for napping, I’d soon have enough to retire.
Posted on: 06 November 2015 by Don Atkinson
I finished university and started earning a living in 1968. A good wage then was £1040pa ie £20pw for a 40 hr week. This worked out at 10/- ph.
Sounds a lot more than 50p per hour
However, petrol was 4/11 per gallon ie half an hour's wage.
Today petrol is about £4.86 per gallon, so £10 ph (£21k pa) might be considered a reasonable starting salary. But not if you have to work 72 or 91 hours to get it !
A price comparison with housing is an even bigger Brain-Teaser !
Posted on: 21 November 2015 by Don Atkinson
12 + 1 = 11 + 2
in more ways than the mathematically obvious............
Ideas ?
Posted on: 21 November 2015 by Steve J
Posted on: 21 November 2015 by Don Atkinson
Originally Posted by Steve J:
spot-on Steve, both the numerals/symbols and the letters.
Posted on: 22 November 2015 by John Willmott
I hope you don't mind if I jump in and play.
I've followed this thread for some time, and, whilst the math is beyond me, I have enjoyed the enthusiasm and pleasure you obviously get from it ..
As you've entered the arena of "quirky" I'd like to submit:
How can one speak (in English) for approximately 2 minutes, without pausing, and not use the letter "a" anywhere in the narrative ?
Posted on: 22 November 2015 by sjbabbey
You could count from one to one hundred (slightly slowly)
Posted on: 22 November 2015 by Don Atkinson
or from minus one hundred through to plus one hundred rather more quickly.
But saying anything for two minutes, without pausing for breath............?
Posted on: 22 November 2015 by John Willmott
Hmm .. pausing for breath was implied .. but not mandatory .. thanks for being so gentle gentlemen ...
Posted on: 23 November 2015 by Don Atkinson
Nice teaser John. good solution sjb.
Posted on: 24 November 2015 by Tony2011
While waiting for my dentist appointment, I noticed that there was a door constantly being opened using only two of the nine (0-9) digits on a digital lock. These two numbers were pressed 5 times in total to unlock the door. Question: how many combinations would I have to try to break the code?
Posted on: 24 November 2015 by Dustysox
Originally Posted by Tony2011:
While waiting for my dentist appointment, I noticed that there was a door constantly being opened using only two of the nine (0-9) digits on a digital lock. These two numbers were pressed 5 times in total to unlock the door. Question: how many combinations would I have to try to break the code?
2:30 dentist time!!
Sorry Tony, couldn't resist!!!!
Posted on: 24 November 2015 by Tony2011
Originally Posted by Dustysox:
Originally Posted by Tony2011:
While waiting for my dentist appointment, I noticed that there was a door constantly being opened using only two of the nine (0-9) digits on a digital lock. These two numbers were pressed 5 times in total to unlock the door. Question: how many combinations would I have to try to break the code?
2:30 dentist time!!
Sorry Tony, couldn't resist!!!!
Can't laugh as everything is comfortably numb!
Posted on: 24 November 2015 by Don Atkinson
Originally Posted by Tony2011:
While waiting for my dentist appointment, I noticed that there was a door constantly being opened using only two of the nine (0-9) digits on a digital lock. These two numbers were pressed 5 times in total to unlock the door. Question: how many combinations would I have to try to break the code?
Being pedantic, 0-9 is actually ten digits...................
Posted on: 24 November 2015 by Tony2011
Originally Posted by Don Atkinson:
Originally Posted by Tony2011:
While waiting for my dentist appointment, I noticed that there was a door constantly being opened using only two of the nine (0-9) digits on a digital lock. These two numbers were pressed 5 times in total to unlock the door. Question: how many combinations would I have to try to break the code?
Being pedantic, 0-9 is actually ten digits...................
My bad! And the answers is....?
Posted on: 24 November 2015 by Don Atkinson
Being even more pedantic ...............these two numbers were pressed 5 times in total.............do you mean :-
you saw the door opened 5 times, and on each occasion the same code (two digits) was used.
or
Each time the door was opened, 5 sets of two digit codes had to be pressed in order to gain entry ?
Posted on: 24 November 2015 by Don Atkinson
Originally Posted by Tony2011:
Originally Posted by Don Atkinson:
Originally Posted by Tony2011:
While waiting for my dentist appointment, I noticed that there was a door constantly being opened using only two of the nine (0-9) digits on a digital lock. These two numbers were pressed 5 times in total to unlock the door. Question: how many combinations would I have to try to break the code?
Being pedantic, 0-9 is actually ten digits...................
My bad! And the answers is....?
Well, I think I would have to try 10*9=90 combinations to be certain of finding the code but you, after watching so very, very carefully...............probably know the code !
Posted on: 24 November 2015 by Mulberry
Hi Tony,
did you see which two numbers were pressed? If this is the case you would have to try 2^5=32 combinations.
Posted on: 24 November 2015 by Tony2011
Apologies. The question was badly put. Every time the door was opened, I could hear the sound of 5 digits being pressed. Judging by the " tone" of the digits, only two "numbers" were being pressed! So, which two numbers were used to open the door?
Posted on: 24 November 2015 by Tony2011
One number was pressed once and the other pressed four times.
Posted on: 24 November 2015 by Tony2011
Originally Posted by Don Atkinson:
Originally Posted by Tony2011:
Originally Posted by Don Atkinson:
Originally Posted by Tony2011:
While waiting for my dentist appointment, I noticed that there was a door constantly being opened using only two of the nine (0-9) digits on a digital lock. These two numbers were pressed 5 times in total to unlock the door. Question: how many combinations would I have to try to break the code?
Being pedantic, 0-9 is actually ten digits...................
My bad! And the answers is....?
Well, I think I would have to try 10*9=90 combinations to be certain of finding the code but you, after watching so very, very carefully...............probably know the code !
Yep. I was bored!
Posted on: 24 November 2015 by Don Atkinson
Ok, so the person who set the code had 10 digits to choose from but only used two digits.
He used the two digits to establish a five-figure code. One digit always features four times in the code. The other digit always features only once.
You listened to the code, much as you would a Morse code and heard eg •−−−− or −•−−− to give two examples.
You attributed these sounds to the equivalent of (say) 47777 or 74777
But you can't remember where (in the above sample sequence) the single digit "4" occurred
Looks like a great brain teaser just to be able to read the question Tony, never mind the answer
Posted on: 24 November 2015 by Tony2011
Originally Posted by Don Atkinson:
Ok, so the person who set the code had 10 digits to choose from but only used two digits.
He used the two digits to establish a five-figure code. One digit always features four times in the code. The other digit always features only once.
You listened to the code, much as you would a Morse code and heard eg •−−−− or −•−−− to give two examples.
You attributed these sounds to the equivalent of (say) 47777 or 74777
But you can't remember where (in the above sample sequence) the single digit "4" occurred
Looks like a great brain teaser just to be able to read the question Tony, never mind the answer
Now now! No need to get personal. I was under the influence of a strong sedative and was not thinking straight. That's my excuse and I'm sticking to it!
Posted on: 24 November 2015 by Dustysox
Originally Posted by Tony2011:
Originally Posted by Don Atkinson:
Ok, so the person who set the code had 10 digits to choose from but only used two digits.
He used the two digits to establish a five-figure code. One digit always features four times in the code. The other digit always features only once.
You listened to the code, much as you would a Morse code and heard eg •−−−− or −•−−− to give two examples.
You attributed these sounds to the equivalent of (say) 47777 or 74777
But you can't remember where (in the above sample sequence) the single digit "4" occurred
Looks like a great brain teaser just to be able to read the question Tony, never mind the answer
Now now! No need to get personal. I was under the influence of a strong sedative and was not thinking straight. That's my excuse and I'm sticking to it!
No, Tony it was my all fault...humour never was my strong point
Posted on: 24 November 2015 by Don Atkinson
Well Tony, now that we've sorted out the question, I think it's a great one !
Suggest you have a look at "the which Wine" thread to pick something tasty to take over when the "...influence of a strong sedative..." wears off.
