Puzzles and Pictures

A puzzle based on a blog post, a solution to an old puzzle, another puzzle from brilliant and some photographs

INTRODUCTION

Earlier today I put up a post titled “About Autism“, and because that post contained so much stuff this post is going to be much smaller – and with only a few links, all in one way or another puzzle connected. 

DERIVING A PUZZLE FROM A BLOG POST

Ester put up a post titled “Year 1729“, which featured the image below:

IMG_0079

The puzzle I am attaching to this is: which two famous mathematicians are linked by the number 1,729 and how did that link come about?

THE SOLUTION TO THE
MARBLES PUZZLE

In a post on Monday titled “Autism, Disability, Mathematics, Religion, Politics” which featured the following problem:
Marble Q

Below is first the answer that I gave, and then one of the solutions posted on brilliant:

answer

This solution from Arjen Vreugdenhil was particularly neat:

solution

NEW PROBLEM: TREASURE HUNT

This is another problem from Brilliant – can you find the treasure?

treasurehunt

PHOTOGRAPHS

PC 2Cormorants and gullstaking the plungeLarge slugCormorants 5Cormorants 4Cormorants and West Lynn ChurchCormorants 3Cormorants 2CormorantsFlying gull agains sunsetFlying gullblack slugtownscape

Wagtail
This time the little wagtail has the shot to itself.

 

 

 

Autism, Disability, Mathematics, Religion, Politics

Various links as indicated by the title of this post, the solution to one problem and a new problem. All topped off with the some photographs.

INTRODUCTION

This post features links, puzzles and pictures. The title refers to the subjects officiallly covered within the post. 

A NEW AUTISM RESOURCE

The Neurodivergent Rebel has produced a post that could become a goldmine. Titled “Web Resources” she describes it as a growing list and ends the post with this:

This is a growing list. Please send suggestions to NeurodivergentRebel@gmail.com

If you can think of anything to help the Neurodivergent Rebel expand this list please use the quote out above, which if you click on it will open up an email message addressed to her which you can then complete.

DISABLED PEOPLE ON BUSES

I have two links in this section. Firstly to a piece from Transport For All about Transport for London’s rExcl: proof faithless council, not union, to blame for Birmingham bin strikeExcl: proof faithless council, not union, to blame for Birmingham bin strikeesponse to the Supreme Court’s ruling on wheelchair priority spaces on buses. This piece is titled “First steps from TfL in response to Supreme Court’s ruling over the Wheelchair priority space on buses” 

Secondly, from Buzzfeed, comes this piece with the self explanatory title “Disabled People Say They Are Still Being Denied Priority Spaces On Buses Despite A High Court Ruling”.

TWO FROM THE SKWAWKBOX

The Skwawkbox is a regular source of excellent material, and these two pieces are no exception:

  1. BHAM COUNCIL MUST NOT BE ALLOWED TO SCAPEGOAT CLANCY TO RENEGE ON BIN DEAL – A follow up to the story that I reblogged from this site recently about a dispute in Birmingham.

  2. The second piece concerns the make up of the Labour Party’s National Executive Committee – the detail contained in the title “EXCL: PRO-CORBYN ASLEF, FBU TO TAKE NEC SEATS” means that at least for the present, and for the very first time, the NEC will have a pro-Corbyn majority. Here is an ASLEF related picture:
    Autism Acceptance Month

SWETA OJHA ON RELIGION

Sweta has produced an excellent poem titled “If Religion Schools You To War” and from it I quote the all-important final verse:

And if –
Religion still schools you to war
I, an atheist deserve an applaud.

MATHEMATICS

This section will include two links, the solution to one puzzle and a second puzzle. Both the links come from the Robert Loves Pi blog, and they are:

  1. A Zonohedron with 7802 Faces –  another of his remarkable constructions using Stella 4D: Polyhedron Navigator.

  2. A Four-Color Flag – exactly what the title suggests, and here is said flag:
    a four-color flag

PUZZLES

On Thursday in a post titled “Links, Pics and Puzzles” I included this puzzle:

Q

The solution is 96% + 96% of 4%. 96% of 4 is (4 x 96)/100 = 3.84. 96 + 3.84 = 99.84, os the answer is that if the death rate in surviving species had been the same as the overall extinction rate then 99.84% of all living things would have died in that event.

For my next puzzle I turn once again to Brilliant and offer up the following:

Marble Q

I will probably provide a solution on Wednesday.

PHOTOGRAPHS

Moorhen in algae

Nar Valley Park
Nar Valley Park – this development is now approaching completion.

gulls3

Town Hall
The next four pictures were taken on Thursday night – I had been acting as stand-in host on my aunt;s behalf, welcoming an airbnb guest to her house, and it was getting dark as I returned.

Lumiere 3Lumiere2lumiere1GullsGlaucous GullFlying cormorantmoorhens

Links, Pics and Puzzles

Lionks to various pieces I have found on the internet, an answer and solution to one problem and a new problem, and some photographs.

INTRODUCTION

This is a sharing post with some of my own stuff as well. I hope you enjoy it.

CROSSBOW BOLT STOPPED PLAY

Play between Surrey and Middlesex at the Oval has been halted and the ground has been locked down because a crossbow bolt was fired from outside the ground into the ground. Everyone at the ground is now in sheltered areas not out in the open. Armed police are now present at the ground. The match has now been officially abandoned, and a controlled evacuation of the ground is now underway.

SCIENCE AND NATURE

First a trio from wildlifeplanet:

  1. “Unreal Photos Of Animals From The Scandinavian Vicious Forest” – a piece highlighting the work of Finnish photographer Konsta Punka taking pictures of forest creatures:

  2. “Beach That Disappeared 33 Years Ago Has Reappeared” 

  3. “Here Is The Bird That Is Able To Fly For 10 Months Non-Stop (Video)” – a piece about the swift.

Hurricane Harvey has quite rightly received a lot of coverage. Here are three of the better pieces:

THE BEST BUS STOP

This bus stop is the subject of a post on illaboratoriodipleeny titled “Una meravigliosa fermata del bus….” that was brought to my attention by Anna, who was as impressed by it as I am. Here is the bus stop:

SOME POLITICAL PIECES

I start with a tool created by the Labour Party called the living wage calculator. You enter your postcode and it tells you how many people in your area would benefit from the minimum wage being increased to £10 per hour. Below is what is says about my postcode:LW

My next two pieces both come from the Skwawkbox:

A SOLUTION AND A NEW PROBLEM

In one of my posts on Monday I set a problem from brilliant. Here is I show the answer and an impressive solution. I also offer a new problem to end the section.

Thomas’ answer:

Screenshot 2017-08-31 at 5.51.15 PM

I admit to being lazy on this one – knowing that the internal angles of an octagon add up to 1080 degrees and that 7 x 90 = 630 I realised that with seven acute angles the remaining angle would have to be over 450 degrees, and the max is just under 360 degrees which takes you back to where you started. However 6 x 90 = 540 which means that the remaining two angles would have to add up to something in excess of 540 degrees, which is no great difficulty. Therefore I gave the correct answer of six (in less time than it has taken me to type this). However, one solver by the name of Atomsky Jahid produced a splendid effort:

Screenshot 2017-08-31 at 5.52.52 PM

A NEW PROBLEM

The mass extinction at the end of the Permian era is at the time of writing officially the largest in Earth’s history. An estimated 96% of all species on Earth at that time were rendered extinct. If the death rate in species that were not completely wiped out had been the same as the extinction rate what proportion of living creatures would have been wiped out in this event?

PHOTOGRAPHS

Guildhall
With Heritage Open Day coming up soon I decided to revisit these first two pics which feature thw town hall.

window

Greyfriars + wm
Greyfriars tower and the war memorial
Library
The library, taken today

P1040565

P1040566
A hald-moon in an early evening sky.
P1040564
The first of three closer up and enhanced shots of the half-moon.

P1040563P1040562Moorhen£2 - end of WWII

Answer to the Pythagorean Problem

The answer to a problem incliuded in yesterday’s post Monday Miscellany.

INTRODUCTION

You may remember that in yesterday’s post titled “Monday Miscellany” I included one of the problems I had solvced on the mathematical website Brilliant – this post presents the solution and also clears up a side issue raised on that website by disgruntled folk who had got it wrong.

THE PROBLEM

Here is the problem again from yesterday:

Pythag

THE SOLUTION

The answer is True. The formula for (x+1)^2 is X^2 + 2X + 1, and every odd number greater than 1 could serve as the 2X+1 part of that equation. 

THE SIDE ISSUE

Some people on Brilliant cavilled at this because there are some Primitive Pythagorean Triples whose smallest term is even (8,15, 17, 20,21,29 and 65,72,97 were all mentioned, although none of the complainers mentioned 12,35,37, 60,91,109 or 696,697,985). The question did not state that the triple of which the odd number is the lowest term was the lowest triple to feature that number, and indeed if one looks carefully at the triangles presented as part of the problem one can see clearly that the odd number is allowed to be in another triple where it is not the lowest term:

Pythagorean Triples Solution - a

Note that the number 5 features twice (ringed in the diagram above, once as the largest term in a triple and once as the smallest).

Thus that 15 features in 8,15,17 does not invalidate the claim of the question since it is the smallest term in 15, 112, 113. All the other odd numbers mentioned in triples of which they are not the smallest member likewise feature in triples in which they are the smallest member, the biggest being 985, 485112, 485113. 

Monday Miscellany

A mixed bag of an offering this Monday afternoon!

INTRODUCTION

This post will be every bit as varied as its title suggests, featuring a mix of politics, mathematics, music, nature and photography (and possibly more). 

SOME MATHS RELATED STUFF

I start with one of more recent followers, RobertLovesPi, and I have several pieces of his to share:

My next piece, courtesy of whyevolutionistrue is titled “The Coffer Illusion“, which concerns the picture below:

If the illusion defeats you, you can find out where the circles are by going to the original post. 

I finish this little section with a nod to the mathematical website Brilliant, which I am a regular visitor to (I am currently on a 64 day problem solving streak). As a sample here is a problem I solved today, rated at maximum difficulty by the site, pretty close to minimum by me:

Pythag

You can look at solutions to this problem on the website, and I will reveal the answer on this blog tomorrow. 

A FEW POLITICAL PIECES

There has been a lot of coverage from various people of events in Charlottesville. I choose to draw your attention to Richard Murphy’s excellent piece on Tax Research UK, titled “Charlottesville is a cradle of extremism: we should take note“. Below is a screenshot of the first few paragraphs:

charlottesville

My second link is to the petitionsite, regarding a young women in El Salvador who having been raped and then had a miscarriage has then been jailed for 30 years due to the Catholic church influence anti-abortion laws of that country. The screenshot below is formatted as a link to take you to this petition to sign and if possible share it:

Screenshot 2017-08-14 at 3.29.29 PM

I finish this section on a lighter note, courtesy of whyevolutionistrue. This little piece titled “Where is North Korea? Some Americans have no idea” reminds us how unacquainted USians are with that area known as the rest of the world! Here is a screenshot of the opening paragraph:
Screenshot 2017-08-14 at 3.39.40 PM

PHOTOGRAPHS

I usually end my blog posts with some of my own photographs, but this photograph section has an additional feature – as a nod to the principal subjects of many of the photos that follow I offer you a musica prelude – Ottorino Respighi’s “The Birds”:

cormorants and boatCormorants8Cormorant headsCormorants6Cormorants4Cormorants3Cormorants2Cormorants1Cormorants and gull 5Cormorant4Cormorants11Cormorants 10Cormorants and gull3TerngullCormorant3Cormorant2

Cormorant
I did not notice the white bird on the far side of the river until I was editing this one – I think from the shape and colour that is a Little Egret but the image is not clear enough to be sure.

Cormorants and swimming gullPollinator3Flybutterfly wingPollinator2white butterflyPollinator

Squirrel does Meerkat impression
This squirrel is clearly an impressionist – and his meerkat is very good!