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 !!
A train can accelerate at 200mm/s² and slow down at 1000mm/s².
What is the minimum time the train can travel between two stations 2 km apart, starting from rest at one and stopping at the other.
Assume there is no Permanent Speed Restriction PSR.
Sometimes a Picture is worth a thousand words.....................
Calcs to follow
Hope you can read my writing...............
........and as Matthew says, just under 2 minutes and 35 seconds
Now, I saw this a few years ago someplace and I know what the published answer was to Part 3. (this kinda gives away the answer to Part 1...........)
However, try as I might, I cannot get the published answer to Part 3. I am always out by a factor of 10. This means that either I am making a consistent mistake, or the published answer is wrong. Frustrating. I am really hoping somebody can help !
The bullets wind up embedded in the thick, solid block. They don't pass through or ricochet.
Hi Don,
Bullet is fired and takes ~0.01s to hit block, think this is the important part. Once the bullet is fired block accelerates to 0.005 m/s as you calcualte. But when the block is reached the sytem stops moving for 0.09s until next bullet is fired. So the average velocity is 0.0005 m/s but it will be a stop start affair.
Thanks for posting the workings, was never my strong point 
Matthew
Ok, not a Brain Teaser, but certainly typical of the old A-Levels about 50 years ago.
I'll have to have a look at some current A-Level stuff soon. No doubt it will cover the details of how digital communication works and interactions between photons and protons and that sort of stuff ?
Hi Ian,
A very good "first stab".
No need for any more stabs. The answer is spot-on. Well done !
Brings back memories ? (or nightmares ?) 
Don Atkinson posted:Hi Ian,
A very good "first stab".
No need for any more stabs. The answer is spot-on. Well done !
Brings back memories ? (or nightmares ?)
Thanks Don,
No nightmares, but my first Brain teaser for a while - I've not been posting here much in the last few years - enjoying life and music too much
For anyone wondering this is one of the many probability problems where it is easier to work out the answer to the inverse problems and then subtract from 100.
The probability of drawing a card that is NOT and ace is 48/52 for the first card, 47/51 for the second, 46/50 for the third and 45/49 for the fourth. Multiplying these together gives a joint probability for having four cards with NO aces of 0.719, so the probability of having at least one ace is 1-0.719=0.281 .
Ian G. posted:Don Atkinson posted:....mealsothinks you guys are correct !! Really well done !!
Does either of you wish to reveal his working ? Mine is based on 1- (prob of not hitting 3x20)
1 - (0.6)n where n = number of throws.
Great minds think alike....
....let's not complete that saying..........
for the benefit of anybody who might be wondering.....this is how I finished it (*)
1 - (0.6)n > 0.9
(0.6)n < 0.1
n log (0.6) < 0.1
n > 0.1/log(0.6)
n > 4.5
hence 5 throws are necessary
(*) but as Nick (and Ian ?) probably did, just keep multiplying 0.6 by itself until it gets smaller than 0.1 ......it takes 5 goes (0.6 x 0.6 x 0.6 x 0.6 x 0.6) to get below 0.1