Good and Bad Mathematical Problems

Two splendid problems, one terrible one and one intermediate one, all courtesy of brilliant.org.

INTRODUCTION

This week on brilliant.org I have encountered two of the finest mathematical problems that I have seen on that site, and also unequivocally the worst. In the rest of this post I will share these problems with you – solutions and explanations will appear in a later post.

FIRST THE BAD NEWS

This is the terrible problem referred to in the introduction. In almost 15 months og being a brilliant.org solver I have complained about precisely one problem – this one:

The “correct” answer when I give it will make it clear precisely why I was so annoyed by the setting of this problem.

TWO FABULOUS PROBLEMS

These two problems were beautifully set, very fun to solve, and one has a published solution that I consider to be quite superb. First:~

I tackled this one this very morning:

A BONUS PROBLEM

Can you give Honey the ant maximum possible access to the surface of the cube?

A Grockle’s Eye View of Cornwall 10: The Map Room at St Michael’s Mount

Continuing my account of my visit to Cornwall. Today we look at the map room at St Michael’s Mount.

INTRODUCTION

Welcome to the latest post in my series about my visit to Cornwall. As part of my coverage of a day at St Michael’s Mount I am devoting a whole post to the map collection there.

A Collection of Antique Maps

For a cartophile such as me this section of the visit was particularly good fun…

Plymouth to Senan — In the days before googlemaps this is what a walking route looked like!

Jan Janssons Cornwall — At one time the Dutch were trailblazers when it came to cartography.

Falmouth – one of the people who have noticed my posts about cornwall is **thecornishbird**, whose offerings include this about Falmouth: **https://cornishbirdblog.com/2018/07/14/things-to-do-in-falmouth/**

A Grockle’s Eye View of Cornwall 9: The Top of St Michael’s Mount and the Descent

Continuing my account of a visit to St Michael’s Mount.

INTRODUCTION

This is the third to last post about the day at St Michael’s Mount, and the ninth in my series about my summer visit to Cornwall. The next post will be all about the vast collection of antique maps that are on show here, and then a final post about the last stages of the day. I then have the journey home to cover to complete the series.

THE REMAINDER OF THE SUMMIT

At the end of the previous post in this series were about to head indoors for the second time in our exploration of St Michael’s Mount…

At this point we entered the map room. As an appetiser for the next post I offer one picture from there…

After the maps came a display featuring large amounts of weaponry…

remains of spiral staircase — The remains of a spiral staircase

Cornish map with extras — A final map, separated from all the others.

That ended the indoor stuff until lunch time.

THE DESCENT

The descent takes past an emplacement of mini-cannons which are of French Revolutionary origin…

Just beyond this I encountered a Red Admiral butterfly:

Red Admiral I — At first it had its wings folded making ID difficult…

Red Admiral III — …but when it opened them out there was little room for doubt.

Not long after this we could see our next destination, where we would be having lunch.

A Grockle’s Eye View of Cornwall 8: Ascending St Michael’s Mount

Continuing my account of my visit to Cornwall, with the ascent of St Michael’s Mount.

INTRODUCTION

Welcome to the latest post in my series about my stay in Cornwall. This post takes us up St Michael’s Mount and covers some of the stuff at the top. There will be at least two and possibly three more posts about the day.

BASE CAMP (!)

Among the places at ground level, before the ascent begins are the restaurant where we would be having lunch and a visitor’s centre which provides a comprehensive introduction. After these one passes through a field that contains a dairy cottage before the ascent begins.

TL2 — No sops for creationists here! The straight truth about the formation of the granite of which the mount consists – it was formed longer before the dinosaurs roamed the earth than we are after the last dinosaurs disappeared.

THE ASCENT BEGINS

The climb up to the buildings on top of the mount begins by way of The Pilgrims Steps, continues past the Giant’s Well and the Giant’s Heart and a cannon emplacement. Then comes the first indoor section and a roof terrace where we pause until the next post in this series…

The vicinity of the Giants Heart — And about 50 yards further along The Giant’s Heart.

Wall mounted militaria I — The first weapons display – in the next post you will see another one.

Garden from above I — Us hoi polloi can only view these gardens from above – we never actually get into them.

Roof terrace — This where our next post will start from.

A Grockle’s Eye View of Cornwall 7: Walking to St Michael’s Mount

Continuing my series about my visit to Cornwall, with the first of several posts about St Michael’s Mount.

INTRODUCTION

This series has been widely spread out – the trip it describes took place between July 12 and 16. Here is a listing of the previous posts:

Getting There
St Germans to St Ives
A Visit to a Seal Colony
The End of the St Ives Day
Crossing the Cremyll Ferry to Plymouth
Historic Plymouth

Having covered Thursday, Friday and Saturday in six posts we arfe now dealing with the Sunday, my last full day in Cornwall.

THE PLAN

As all five of us (my parents, my sister and my nephew as well as me) were making the visit to St Michael’s Mount we travelled in my parents camper van instead of using the train. We wanted to be underway by eight and achieved this. We were planning to explore St Michael’s Mount in full and then have lunch at an establishment there. Things panned out pretty much as intended. The road journey is a lot less scenic than the rail equivalent, so I am going to recommend unequivocally that anyone else planning to do this use the train – the walk from Penzance (all of which is familiar to me, although we started part way along it, having located a parking place just outside Penzance) is very scenic, while there is a longer walk available from St Erth (inland for most of its duration, instead of along the sea front). Here are a couple of satellite views:

Penzance - St Michael's Mount — The coastal route starting from Penzance.

St Erth to St Michael's Mount — The longer and mainly inland route starting from St Erth. This map also features what is in alphabetic terms the last place in Britain.

THE JOURNEY IN PHOTOGRAPHS

This section ends the post, taking us across the causeway to the base of the mount:

View from the van — The only shot I managed to get from the van on the way from Fort Picklecombe to Penzance.

People crossing the causeway to the mount — A first glimpse of the causeway.

In the shallows — From Marazion the quickest way to the causeway is straight across the beach, and in the heat walking barefoot through the shallows was the way to go.

The causeway and the mount — The causeway.

Standing Up For Nature

Sharing a number of nature themed campaigns.

INTRODUCTION

My twitter feed today has had many links to campaigns relating to nature, so I have decided to share the featured campaigns here as well. First to set the scene here is…

AN OPEN LETTER TO LEADERS

I shared this when Anna first posted it but it deserves further exposure, and ties in beautifully to the theme of this post (nb all screenshots in this post are formatted as links – click on them to visit the originals).

NATURE THEMED CAMPAIGNS

Protect Crayford Marshes:

2. Save the trees at Roath Mill and Roath Brook Gardens:

3. Save our Forests:

4.Call for an immediate ban on South Africa’s trade in lion body parts:

5. Save Gwent Levels:

6. Save Arundel’s Countryside from Bypass Ruin. This one is a crowdfunder, but since I do not have money to give I am settling for giving it wider exposure:

7. Last but by no means least comes a call to ban the vile practice of trophy hunting:

Hat tip: @team4nature twitter account.

A Grockle’s Eye View of Cornwall 6: Historic Plymouth

Continuing my account of my most recent visit to Cornwall.

INTRODUCTION

Yes, Plymouth is Devon not Cornwall, but my visit to the town was part of my stay in Cornwall, so it belongs in this very spread out series of posts.

THE WAR MEMORIAL

This particular memorial honours those lost at sea as well as those killed in war, because Plymouth is very much a naval town.

Memorial - distant view — A first, distant view of the memorial

Memorial base — A series of close-ups – each vertical bronze panel around the base is a list of names.

OTHER PICTURES FROM HISTORIC PLYMOUTH

There were plenty of other things to see around the sea-front…

Circualr paving pattern — A quirky pavong arrangement…

Eddystione Lighthouse — …and an explanatory plaque

AN ITEM OF SHERLOCKIANA

It will be no news to followers of this blog that I am a fan of the world’s first and greatest consulting detective, so it was pleasing to acquire a photograph with a connection in that direction:

One of Holmes’ most famous cases takes place on Dartmoor, not far from Plymouth.

THE RETURN CROSSING

It was now time to recross the county boundary into Cornwall, one again on the Edgecumbe Belle.

Open letter to all Leaders: Time’s up

Originally posted on Annas Art – FärgaregårdsAnna:
If you wanna spread this letter, you are welcome to share it worldwide. Tag it with #timesup if you want. If you want to make a translation of the text to other languages and share it, do it. We all have to help out saving our…

Please read and share Anna’s wonderful open letter to leaders. Note that this is Anna’s work and that therefore I am closing comments, as those should go direct to the original.

Annas Art - FärgaregårdsAnna

If you wanna spread this letter, you are welcome to share it worldwide. Tag it with #timesup if you want. If you want to make a translation of the text to other languages and share it, do it. We all have to help out saving our planet. This is one way among millions to help.

The image is free to share.

Anna

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A Grockle’s Eye View of Cornwall 5: Crossing the Cremyll Ferry to Plymouth

The latest installment in my series “A Grockle’s Eye View of Cornwall”. This starts my coverage of Saturday in Plymouth.

INTRODUCTION

My nephew needed some things that we had to go to Plymouth for, and so he, my mother and I took the Cremyll ferry to Plymouth, attended to the shopping and then went up on to The Hoe (subject of my next post).

THE CREMYLL FERRY

Once we were safely aboard the ferry it was time for the camera to do its work:

THE SHOPPING PART OF THE EXPEDITION

We had a substantial walk from the ferry terminal on the Plymouth side to the shopping area, during which I saw a few things to photograph:

The first (or last) pub in Devon — Depending on your viewpoint this is…

Twin signs — …either the first or last pub in Devon

**The Greedy Goose**, this is also the oldest house in Plymouth. I did not get to eat here, but it is a splendid building.

Press Releases and Triangular Bridges

Some stuff about upcoming auctions and press coverage thereof and the solution to my most recent mathematical teaser.

INTRODUCTION

This post deals with some of my work at James and Sons and also includes a solution to a problem I posed last week.

PRESS RELEASES

In my recent post about James and Sons’ upcoming gold coin and proof set auction I included a copy of the official press release I had put out about it. What I did not mention in that post is that we also have a less significant ajuction coming up this Monday, for which I had also out out a press release. Both are reproduced below to set the scene for what follows:

On Thursday morning I checked into the James and Sons twitter account and was delighted to spot a link to an article in the Fakenham and Wells Times (part of the Archant stable and therefore connected to the Eastern Daily Press) about the coin auction. Below is a scan of the print version of this article:

Then yesterday morning brought more positive news – a link to an article in that day’s Lynn News about Monday’s general collector’s auction. The focus of this article is some documents we have relating to William Hoste, after whom The Hoste in Burnham Market is named, and who was a protege of Lord Nelson and connected by marriage to Robert Walpole. Here is a scan of the print version of this article:

We have another auction in preparation, and I have already pretty much decided that this 19th century presentation conductors baton (it is too large to have been intended to be used) will be the feature image in the press release for that one:

11-a — For me the local connection revealed here clinches it.

THE TRIANGULAR BRIDGES

Here is the problem I set last week, followed by the answer and an official solution:

Here is a concise solution, courtesy of Chew-Seong Cheong :

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