carrying out the subtractions in thte brackets above gives us (2 * 3^22)(2 * 3 ^23)(2 * 3^24). This becomes (2^3)(3^(22+23+24))= (2^3)(3^69). Thus m = 3 and n = 69, and 69 + 3 = 72.
As a supplement to this little problem, would you have an observation platform where the three bridge segments meet at the centre of the lake? This latter of course, unlike the mathematical question is purely a matter of opinion. I would go for a circular platform just below the level of the bridges, accessible by lifts and stairs.
A solution and two new problems by way of a quick post before setting off for Marxism 2018.
I am writing this immediately before setting off for Marxism 2018, a four-day political festival taking place in London. I should be able to do some posting at the event and at my accommodation. In my recent “An A-Z of Me” I included a mathematical problem from brilliant.org, and I now post the solution to that problem and offer you a couple of others.
The problem I posted earlier was this:
The answer is that there is not, because it turns out that the perimeter of a plus-plus is always a multiple of four, which 2018 is not.
TWO NEW PROBLEMS
These are also both from brilliant.org. One is easy but generated a bit of controversy, while the other is very hard to solve properly, but by applying logic it can be easily worked out what the correct answer is. First, the hard problem:
The easier problem which generated some controversy is this one:
Notice of my imminent departure for a week’s holiday and solutions to Wednesday’s puzzles.
A couple of days ago I set some puzzlesfor you, and in this post I will be answering them. Also, I am off to Greece for a week’s holiday later tonight (I fly out of Gatwick at 5:40AM, so am envisaging taking the 21:36 train out of Lynn, connecting to a Thameslink service at St Pancras and arriving the airport just after 1AM – the second latest set of connections available to me, and I know British public transport too well and trust it too little to rely on the last possible connections) and although I will take any opportunities that arise to go online I will still have comparatively little access to the internet, so you will hear little from me between now and a week tomorrow evening when I shall be back home.
SOLUTION 1: DR FRANKENINE
Here is the most elegant of the official solutions, posted by Callum Cassidy-Nolan:
SOLUTION TWO: FUEL TANK
As you can see from the above graphic, almost half of those who attempted solutions on brilliant.org got it wrong. A perusal of the comments section revealed a degree of reluctance on the part of some of the errant solvers to admit to being wrong (never mind arguing with the umpire, some of these folk were metaphorically following that up by arguing with TV replay umpire) so I am to explain the whole process of getting the right answer (though it took me milliseconds to work out and not much longer to enter the correct answer):
After stage 2) half of the original fuel remains and is then topped up with new fuel, and we are told to assume that perfect mixing occurs…
After stage four one quarter of the tank of perfectly mixed fuel has gone, and as it is perfectly mixed one half of that fuel is original, meaning that a further one eighth of total tank full of original fuel has been used.
One half plus one eighth = five eighths of the original tank full of fuel has been used, leaving three eighths of the original tank full still there.
As a percentage three eighths is 300/8 = 37.5 per cent, and the question has asked for that figure.
One particularly offensive complainant attempted to use the fact that the question had said decimals allowed to claim that an answer of 0.375 should have been permitted. This is wrong – the question specifically asked for a percentage, and the reason for mentioning the a decimal figure was OK was so that people did not think they needed to round to the nearest whole number, which in correct mathematical notation would have been 38 (the figure being rounded away is five or greater so you round up, had it been four or less it would have been correct to round down).
Another complaint people made was being marked wrong for including the percentage symbol – I am less unsympathetic to this than I am to the indefensible claim that 0.375 should have been marked as right, as this latter has missed out turning the answer into a percentage, but including the symbol is still a mistake as the way the question is asked renders it needless to do so.
Please note that I did not create this problem and had nothing to do with deciding what answer should be marked as right – I have treated it at length because I was annoyed on the composers behalf that so many solvers rather than attempting to see by looking at correct solutions, of which plenty of good ones were posted, why their chosen answer was wrong instead opted for the ‘argue with the umpire’ approach, in some cases being very unpleasant about it. Here to end this little post is David Vreken’s published solution:
An overview of Heritage Open Day 2017 and the solution to a mathematical problem.
Yesterday was Heritage Open Day in KIng’s Lynn, and as readers of this blog will know I was one of the volunteers helping to run the event. This post is a scene setter, giving an overview and indicating which parts of the day I will be giving individual posts to later on. At the end of this post I will include the answer the puzzle I posed at the end of my previous post.
STARTING THE DAY
I was going be stewarding at 27 King Street from 12 until 2, and knowing that I would find that experience a draining one I decided to see a handful of places before 12. The first place I visited was the one I had marked down as “must see”, because it was probably the only time the opportunity would be there do so –
NO 2 HAMPTON COURT
This property being currently vacant and of considerable historic interest it was open, and within was a little local history exhibition as well as the place itself. I will be giving this a dedicated post, so here for the moment is a single picture to whet your appetite:
I decided to head for King Street by way of the river front, and between this property and the river front is…
THE SECRET GARDEN
I knew that my aunt would be running things in this garden, so a quick visit seemed in order.
The main attraction (especially as the cockling boat Baden Powell was absent) down at the river front was, as on previous occasions…
THE IFCA RESEARCH VESSEL
IFCA stands for Inshore Fisheries and Conservation Authority, and their remit is to insure that population levels of sea creatures living within six nautical miles of the shore do not decrease too dramatically. I will be creating a dedicated post about this, so I offer this picture as bait…
My plan on leaving this vessel was to…
PAY A PRELIMINARY VISIT TO 27 KING STREET
I deemed it sensible to familiarise myself with the building that I would be stewarding, so that was my next port of call. As I was at the river front I decided to go by way of the Lower Purfleet, where there was sure to be something interesting happening…
THE TUESDAY MARKET PLACE AND ENVIRONS
After my preliminary look around No 27 King Street I had half an hour to spare, so headed in the direction of the Tuesday Market Place. I paid calls at three buildings in that area, Bishop’s Lynn House, St Ann’s House and St Nicholas Chapel before heading back to no 27…
VOLUNTEERING AT 27 KING STREET
I arrived back at no 27 a few minutes early. My fellow steward for the 12PM to 2PM slot turned out to be veteran councillor Lesley Bambridge. As I will be writing a dedicated post about this I will say no more here. For a picture, here is a quirky architectural feature:
A CLUB ON FERRY LANE
After finishing at 27 King Street I made my next port of call the Ouse Amateur Sailing Club, where I consumed a pint. After that I decided it was time to call it a day as I was unsurprisingly feeling ‘peopled out’ – 27 King Street attracted a lot of visitors while I was there. Here is a picture taken while at the club:
There at least three areas of mathematical knowledge that would give you an ‘in’ to this one – logarithms, compound interest and Pascal’s triangle. Since I have some knowledge of all three this problem barely brought a crease to my brow. Here are a couple of good solutions from others:
The second solution I am sharing here had a particular appeal to me:
Just to finish, the exact power (in terms of positive integers) of 101 that is the the first to begin with a number other than 1 is 70, and 101 ^ 70 runs to 140 digits.