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: 28 June 2016 by Don Atkinson
Hi Frank,
yep, 4 minutes it is.
"Some people in this great country of ours can run a mile in four minutes".......( that was the response from Col. Blimp when asked about the benefits of the Fylingdale 4-minute nuclear warning)
Posted on: 28 June 2016 by Don Atkinson
The yellow circle just fits inside the red square.
The corners of the blue square just touch the circumference of the yellow circle.
What fraction of the area of the red square is the area of the blue square ?
Posted on: 28 June 2016 by hungryhalibut
Posted on: 28 June 2016 by Don Atkinson
Is that you ?
or Henry.................
Posted on: 28 June 2016 by hungryhalibut
That was me! Henry is swatting for his D2 tomorrow - his last A level paper - and 'cannot be disturbed'.
Posted on: 28 June 2016 by Don Atkinson
Well done Nigel. Spot-on.
There is an easy way to see the answer and a more "conventional" way.
I'm wondering how many people can see the easy way.
And all the best for Henry tomorrow and all his exams.
Posted on: 28 June 2016 by sjbabbey
The length of a side of the large square is equal to the diameter of the circle and by extension also equals the length of the diagonal of the smaller square.
If we assume the length of the diagonal etc. to be square root of 2 then the area of the large square equals 2 sq units and by Pythagoras the sides of the smaller square equal 1unit each giving an area of 1 sq unit or half the area of the large square.
Posted on: 29 June 2016 by Don Atkinson
Sometimes a picture is worth a thousand words.
I rotated the yellow circle (with the blue square firmly attached) through 45 degrees.
Posted on: 29 June 2016 by Christopher_M
Posted on: 29 June 2016 by Don Atkinson
Back to the simple basics. Just to flex the grey matter, before things get harder
Each of the three different symbols has a different value associated with it. Adding up the value of the symbols in each row and column gives you the value for that row or column. What is the value of each symbol and what is the missing value of the column ?
Posted on: 29 June 2016 by Don Atkinson
Posted on: 29 June 2016 by JRHardee
Posted on: 29 June 2016 by sjbabbey
40
Plane - 7
Train - 19
Ship - 32
Posted on: 29 June 2016 by Don Atkinson
Sorry JR, it looks like SJ has it. Nice try, and well done to SJ.
Posted on: 29 June 2016 by Don Atkinson
On reflection JR, whilst SJ has the same answers that I have, it is possible that you also have a correct, but somewhat different solution to both of us. I haven't checked that possibility.
Posted on: 29 June 2016 by Don Atkinson
Slightly different, and I found it slightly harder.
There are four different symbols to find this time round. Plus the missing column.
Posted on: 29 June 2016 by sjbabbey
An odd one this (I get a negative value of minus 21 for the Green Tick symbol) a value of 33 for the missing column.
Green X = 30 , Green Tick = -21 , Red X = 45 , Black Tick = 63
Posted on: 29 June 2016 by Don Atkinson
I have a solution in which all the values are positive.
I will re-check in case I have made an error in the initial post/picture but I don't think I did.
I know when I was trying to figure out the solution, I felt at one stage I had a conundrum. I can't recall exactly what the conundrum was but it was along the lines that a "tick" was bigger than an "X" by (say) 9, I then found another line which suggested a "tick" was bigger than an "X" by (say) 17. Anyway, the conundrum seemed to evaporate. I now only hope it wasn't real !
I am mindful that JR came up with a different answer to the last one, and although I can't figure out a solution based on 16, it's quite possible that the solutions are not unique ! eek !
Posted on: 29 June 2016 by Don Atkinson
An odd one this (I get a negative value of minus 21 for the Green Tick symbol) a value of 33 for the missing column.
Green X = 30 , Green Tick = -21 , Red X = 45 , Black Tick = 63
SJ, those figures don't seem to add up to column 1
Posted on: 29 June 2016 by sjbabbey
Don, my solution is definitely wrong. Whilst the values work OK for the row totals, it's clear that they give a wrong total for column 1.
Yes, I've just spotted that.
Posted on: 29 June 2016 by DavidDever
The missing column is 93, given the following solution:
green X = 15
green tick = 24
red encircled X = 30
black encircled tick = 48
Posted on: 29 June 2016 by JRHardee
I didn't get a different correct answer.
Posted on: 29 June 2016 by Don Atkinson
The missing column is 93, given the following solution:
green X = 15
green tick = 24
red encircled X = 30
black encircled tick = 48
Hi Dave, Those are the numbers I got. Phew, I thought I might have screwed up.
Well done !
Posted on: 29 June 2016 by Don Atkinson
Don, my solution is definitely wrong. Whilst the values work OK for the row totals, it's clear that they give a wrong total for column 1.
Yes, I've just spotted that.
Pretty good try though, and this together with JR's contribution certainly got me checking my own work !
Posted on: 29 June 2016 by Don Atkinson
I didn't get a different correct answer.
Hi JR,
Thanks for letting me know ! I have now recovered the courage to publish the next one which I had started re-checking just in case there is more than one solution...............i'm pretty sure there is one and only one solution, but we'll soon find out.
