India Take T20I Series

A look at today’s events in Ahmedabad, a mathematical challenge, a new nature themed project and some photographs.

I have a couple of bonus features as well as an account of goings on in Ahmedabad today.

THE PRELIMINARIES

England were unchanged once again, while India chose to give themselves an extra bowling option, selecting T Natarajan in place of KL Rahul. Kohli moved up to open with Rohit Sharma. Eoin Morgan won the toss and chose to bowl.

THE INDIAN INNINGS

Rohit Sharma batted magnificently, scoring a rapid 65, getting out when seemingly nailed on for a century and more. Kohli played the anchor role to perfection and there were explosive contributions from Suryakumar Yadav and Hardik Pandya, promoted on account of his big hitting. India reached 224-2 from their 20, with no England bowler escaping. The highlight for England in the field was a dismissal that appears in the scorebook as C Roy B Rashid, one of the most misleading such entries in cricket history – the wicket was in fact almost solely down to Chris Jordan who ran round the boundary, made an amazing catch and had the presence of mind to realize that his momentum was taking him over the rope and the skill to lob the ball to Roy before that happened. It was a piece of fielding genius to stand with any in the game’s long history.

THE ENGLAND RESPONSE

Roy fell early, but Buttler and the much maligned Dawid Malan batted well for a time, and kept England in the hunt in the process. Both went past 50, Buttler making 52, and Malan going on to 68, in the process of which he became the quickest ever to complete 1,000 T20I runs, getting to that landmark in his 24th innings in that form of the game, two innings fewer than the next best, Babar Azam. However, both were out in quick succession and England soon dropped out of the hunt thereafter. In the end they were 188-8 from their 20, beaten by 36 runs. The crucial intervention on a day which saw 412 runs scored came from Bhuvaneshwar Kumar who took 2-15 from his four overs. Absent him 397 runs came of 36 overs, a rate of 11.03, while he went for 3.75 per over. He has quite correctly been named Player of the Match. More details of today’s events can be found here.

A MATHEMATICAL TEASER

As so often with these, my source is brilliant.org, but I am being a little unorthodox this time – they changed the wording of their question following complaints, and I am reverting to the original:

You can see this question in its original setting here, but I also have two subsidiary questions: a) what complaints do you think led to the wording being changed? b) Were those complaints actually valid given that this was posed as a mathematical not a philosophical question. Full explanations and answers on Monday.

NATURE AND PHOTOGRAPHS

As a segue into my usual sign off, I include a link to a twitter project being run by my friends Team4Nature. Below is a screenshot to explain things, while the tweet can be seen by clicking here.

Time for my usual sign off…

England Re-establish Lead in T20 Series in India

An account of India v England yesterday, some stuff about the environment, a mathematical teaser and a bumper crop of photos.

Yesterday the third of five T20Is between India and England took place in Ahmedabad. The first part of this post gives an account of proceedings in that match, and then I have a couple of bonus features as well as my usual sign off.

THE PRELIMINARIES

For England Mark Wood was fit again and came back into the side in place of Tom Curran, and that was the only change. For India Rohit Sharma returned to the ranks and Suryakumar Yadav who had not even batted on his debut was benched to make way for him. England won the toss, and with the series 1-1 and both matches won by chasing sides, chose to bowl first, the correct decision (although if he wins the toss tomorrow he should gamble and bat first as there as World T20 Cup coming up in India and England will probably need to win at least one match batting first to lift that trophy).

THE INDIAN INNINGS

England bowled magnificently in the Power Play overs, restricting India to 24-3 from the first six overs of their innings. After 15 overs India were 87-5, but they then had what would prove to be their only good period of the match, plundering 69 off the final five overs of their innings to post 156-6 from their 20 overs. Half of this total came off the bat of Virat Kohli. Mark Wood, at his best, had 3-31 from his four overs, and 16 of those runs were hit off the third, fourth and fifth balls of his final over. Every other bowler contributed to a fine team effort, with Rashid being wicketless but bowling his full four overs for 26 runs.

THE ENGLAND RESPONSE

Roy fell cheaply after successive good scores in the first two matches, but Buttler underlined his status as England’s finest white ball batter, looking in complete command right from the start of his innings. Malan got a start, but on this occasion did not turn it into anything big, though he still managed to contribute to a fifty partnership. Bairstow, a superb white ball batter, joined Buttler, and these two players were still together when the match was won in the 18th of 20 overs, Buttler 83 not out off 54 and Bairstow 40 not out off 26 balls. None of the Indian bowlers looked terribly threatening, and Yuzvendra Chahal, their chosen leg spinner, looked leagues below Adil Rashid. Washington Sundar is an economical off spinner, but what India desperately needed and could not get were wickets. A total of 180 might have been defendable by keeping things as tight as possible, but 156 was never. likely to be defended unless India got wickets, and a lot of them. Buttler, who had also done well with the gloves, was the only conceivable candidate for Player of the Match.

THE REMAINING FIXTURES

Although some people either through mischief or through idiocy were questioning Malan’s place in the England side based on two comparative failures the truth is that there are only two changes at present that would make any real sense, and I would be disinclined to make either while the series remains live: Moeen Ali to replace either Sam Curran or Chris Jordan, giving an extra spin option, and/or Liam Livingstone to replace Stokes as no5 batter and sixth bowling option (he can spin the ball both ways, although he is not a regular bowler).

For India things are more complicated – their top order batting has struggled in this series, with fatally poor starts in the first and third matches and an indifferent one in the second, and the bowling attack as currently constituted is simply not good enough. He did not fare too badly this time, but for me if he is going to be worth his place Hardik Pandya needs to be batting in the top half of the order and being India’s sixth bowler, not their fifth. I do not see how Chahal can retain his place – he is leaking runs consistently and rarely threatens to take wickets. The obvious struggling batter is KL Rahul, with one run in his last four innings (note to Malan bashers – that IS the sort of form on which you can talk about dropping a highly ranked batter.

ENVIRONMENT THOUGHTS

The Green Party candidate in the London Mayoral election, Sian Berry (please, Londoners, do the right things this time and elect her) has proposed the creation of a ‘habitat crime unit’ which would tackle habitat and ecological crimes in the capital. I think this is an excellent idea. You can read full details of it by clicking here.

The London Parklet campaign today tweeted out a superb graphic created by Emma Paxton on redesigning cities to be greener. You can see the tweet by clicking here, and I present a screenshot of the graphic below:

A MATHEMATICAL TEASER

I have not presented one of these for a while, but I enjoyed solving this one this morning:

This was originally set as a multiple choice question, but I am not giving readers that luxury, although you can see it in it’s original setting by clicking here. Solution in my next post.

PHOTOGRAPHS

Now it is time for my usual sign off, including my first blue tit of 2021…

England Selectors’ Ostrich Impression and Other Stuff

Some thoughts on the (in)action of the England selectors this week, some mathematical teasers and a few pictures.

INTRODUCTION

A couple of days ago I wrote about England’s series win over India and presented some problems and solutions. This post is on similar lines, dealing with the actual behaviour of the England selectors and my thoughts thereon.

AN OPPORTUNITY SQUANDERED

England, with the series already in the bag, had a diamond-encrusted golden opportunity to experiment with options to fill gaping holes in their top order. Cook’s announcement of his impending retirement from international cricket should have acted as an extra spur. Instead of which we see very little in the way of forward planning or of experimentation of any sort. Even with the certain knowledge that a new opener will have to come in to replace Cook the selectors persevere with the proven failure Jennings.

Three individuals who can feel more aggrieved than most by this behaviour are Rory Burns (another 90 against Essex yesterday after the latter won the toss and chose to bowl first), Dan Lawrence and Liam Livingstone

In view of Cook’s impending retirement I would have recognized openers at 1,2 and 3 (not a bad approach in test cricket anyway), with a view to the two other openers than forming a partnership in future matches. This is why in the previous post I mentioned Tammy Beaumont, a recognized opener who has been scoring stacks of runs recently. Batting is at least as much about timing and placement as it is about brute power, and that is why I believe (unlike in the case of fast bowling) a woman could mix it with the men even at the highest level, similarly with slow bowling and possibly wicket-keeping (for my money the best user of the gauntlets in world cricket across the board at the moment is Sarah Taylor). A number of the all-time greats of test match batting have been of diminutive stature (Bradman, Gavaskar, Tendulkar, Sehwag, Hanif Mohammad and several of the finest Sri Lankans spring to mind instantly). I am well aware that this super-radical option will not happen, but the alternatives that that leaves with are:

  1. Two brand new openers, neither of whom have any experience of international cricket.
  2. One new opener and one opener who has shown already that they are not actually good enough (Jennings)
  3. Two openers who gave failed to prove themselves (presumably Jennings and a recalled Stoneman). 

Of those three options, none of which massively appeal, my choice would number 1, which might end up working out well, and then the question is who to choose to open alongside Burns (whose case for selection is undisputable in the circumstances). 

Having taken the “ostrich option” re their top order difficulties the only outcome from this game that could be acceptable is not merely a win to make it 4-1 for the series but a win by a massive margin. The timidity of the England selectors means that at least one and possibly two England openers will be starting their careers on overseas tours, with their first home test series being against those well known softies, the Aussies.

PROBLEMS AND SOLUTIONS

I will start as usual with answers and solutions to the previous problems (all from brilliant.org) before offering up some new problems.

WHAT IS THE AREA OF THE QUADRILATERAL

Screenshot 2018-09-03 at 5.08.56 PM

First the answer:

quad answer

The hackers solution is that there are only two really serious possibilites since the shape is a square, namely 67 (giving an area of 289 = sides 17 units long) and 102 (giving an area of 324 = sides 18 units long), and since the question gave one three tries just enter those values for the first two tries (if your first entry does not come up right). Here, courtesy of Jeremy Galvagni is an elegant genuine solution:

quadsol

THE .99 STORE

First the answer:

Screenshot 2018-09-05 at 3.09.42 PM

The figure in front of the .99 part of the price can vary, so all we need to know is how many .99s add up to answer ending in .89, and the answer is 11 (11 x 99 = 1,089, so 11 x 0.99 = 10.89), and the next number of items after 11 that would give us an answer ending in .89 is 111, the lowest price total for which would be $109.89. Thus Marie purchased 11 items.

NEW PROBLEMS

First an astronomy themed problem:

astroproblem

Now a question that has got almost three-quarters of those who tackled in on brilliant, but is not actually difficult:

Bullets

PHOTOGRAPHS

Swimming MoorhenMoorhen on branchTwo MoorhensMoorhensMagpie

Cricket and Other Stuff

Cricket, in the course of which I make a very radical suggestion for dealing with England’s top order woes, and a few other things, including Maths and Public TGransport.

INTRODUCTION

As well as some stuff about the state of play in the current England vs India series I have a couple of mathematical problems for you and some of my own photographs at the end.

ENGLAND’S DREADFUL START

England won the toss yesterday morning before the fourth test match of the five match series against India at the Ageas Bowl, Botley Southampton. This was the last thing they managed to do right for some considerable time. At last, with the scoreboard reading a barely credible 86-6, Sam Curran, inexplicably dropped from the last test match and now returning to the fray, emerged from the pavilion. Much of the carnage was more due to good Indian bowling than bad batting, although Jennings (already on borrowed time for my money) will not want to see replays of his LBW (however good a piece of bowling it may have been padding up to one which would have uprooted the middle stump otherwise never looks good). Fortunately England’s tail managed to produce a diplodocid (see picture at end of this paragraph) proportion of the innings. Curran, making the ridiculous decision to drop him from the previous game look positively ludicrous, racked up 78 before he was last out, the total hvaing reached a semi-respectable 246.

Diplodocus
This is why I described the contribution of the England tail as being of diplodocid proportions.

India are currently 135-2 in response. Only once in test match history has a side come back from 0-2 down to take a five match series, in 1936-7 when Australia’s comeback was fuelled by scores of 270, 212 and 169 from Don Bradman in the course of those last three matches. In 1894-5 Australia levelled the series at 2-2 after being 0-2 down but Andrew Stoddart’s England rallied to win the decider. 

England’s continuing top-order woes need to be addressed if they are to avoid surrendering a series on which they seemed nto so long ago to have a vice-like grip. Rory Burns must come into the side in place of Jennings. I would also bring Pope back but place him lower in the order. brief interjection – BIG NEWS – Kohli Is Out! Also, thinking about the need for top order runs I now tender a suggestion far more radical than Rory Burns – there is one England opener who has making stacks of runs all over the place of late – the one and only Tammy Beaumont! The way they have performed thus far none of the current top order are entitled to object to that suggestion.

Beaumont on the attack

Yes going with two new openers would be a colossal gamble, but they could scarcely fare much worse than Cook and Jennings have in this series.

A COUPLE OF MATHEMATICAL TEASERS

Both of these, from my usual source,  are very easy problems which have tripped a number of solvers up. I give them in the reverse order to which they appeared:

Canteen problem.jpg

And

1,001.jpg

HERITAGE OPEN DAY

Heritage Open Day this year is Sunday September 16th. There will be some 60 sites open in the King’s Lynn area, and if you there on the day do make sure you visit. If you happen to visit the cellars at the Bank House between 12 noon and 2PM I will be one of the volunteers you encounter.

TWO STORIES OF BRITISH PUBLIC TRANSPORT DAFTNESS

I start this section with the more minor but also more personal of these stories. Today I made my travel arrangements to Sheffield for a cousin’s wedding. I checked bookings from King’s Lynn to Sheffield, and the cheapest ticket would have cost me £68.20. Knowing that a ‘plan B’ was available I then checked out bookings from Peterborough to Sheffield and lo and behold up came a ticket for just £38.50, which when the two bus tickets on the ExCel are added in amounts to £51 all up. In other words to have travelled by train from King’s Lynn all the way to Sheffield would have cost me 33% more than the combined bus/ train route I am actually taking. Now of course not everyone booking this journey would have known of the alternative, and I wonder how many people have been swindled in this. 

My second story of public transport daftness is that The Elizabeth Line (aka Crossrail) will not now be coming into service until nearly a whole year later than planned (more here).

PHOTOGRAPHS

The pictures here are of items I purchased at our auction on Wednesday (it was reasonably successful, with a few big sales, and a lot of items finding buyers).

121
Lot 121 – I scanned these items rather than photographing of them.

121-a121-b

Under a viaduct and over a bridge
A photograph of the item taken this morning

148148-a148-bBlizzard conditions

360
Two of the four items in this lot were of sufficient interest for me to consider bidding, the Nobel Prize cover, and the one that really settled it, the Classic Locomotives.

360-a360-b

Classic Locomotives FDC
The main cover photographed this morning.

Classic Lcomotives stamps II
The first of two close-ups of the stamps (the reflectivity of the protective covering makes this a challenge).

Classic Locomotives stamps I

Classic Locomotives other side
The ‘cover’ part of this item contains a lot of information when opened up (see also next picture for the other side).

Locos fact sheet

 

A Solution and Some New Problems

A solution and a couple more problems from brilliant.org.

INTRODUCTION

On Wednesday I left you with a problem from brilliant.org to tacke having presented solutions to several others. Today I start with a solution and then present you with some new problems.

SOLUTION TO WEDNESDAYS PROBLEM

Here is the problem again:

Fermat Challenge

Here is the answer:

Fermat answer

And now here is Mark Hennings’ published solution:

Hennings

As a side issue various commenters on brilliant.org demonstrated their failure to read the question by bringing up examples of numbers that are both square and cube (e.g 64), but these are utterly irrelevant since the question was about a number that is both one more than a square and one less than a cube.

NEW PROBLEMS

Two new problems for you, one easy, especially if you are familiar with the story of Signor Malfatti, and one slightly more difficult but quite fun.

CAN YOU OUTDO MALFATTI?

Malfatti Mistake question

SPACE STATION DODECAHEDRON

Space station Dodecahedron

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:

bad problem

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:~
Mendrin Circles

I tackled this one this very morning:

Mr Mediocre question II

A BONUS PROBLEM

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

Honey the ant

Walk for Wildlife

Advertising the Walk for Wildlife and attending to mathematical matters.

INTRODUCTION

The centrepiece of this post comes courtesy of the team4nature twitter account. I have also included the solution to a prnblem from brilliant.org and a new problem from the same source.

WALK FOR WILDLIFE

Walkforwildlife

A SOLUTION AND A NEW PROBLEM

Here is the answer the problem I posed last week:

3 and 2 answer

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.

bridging the lake

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 A Couple of New Problems

A solution and two new problems by way of a quick post before setting off for Marxism 2018.

INTRODUCTION

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 SOLUTION

The problem I posted earlier was this:

plus-plus

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:

clock problem

The easier problem which generated some controversy is this one:

Guards

Answers to Puzzles and Notice of Absence

Notice of my imminent departure for a week’s holiday and solutions to Wednesday’s puzzles.

INTRODUCTION

A couple of days ago I set some puzzles for 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

Dr Frankenine

Here is the most elegant of the official solutions, posted by Callum Cassidy-Nolan:

CCN

SOLUTION TWO: FUEL TANK

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):

  1. 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…
  2. 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.
  3. 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.
  4. 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:

DV

Heritage Open Day 2017 – Overview

An overview of Heritage Open Day 2017 and the solution to a mathematical problem.

INTRODUCTION

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:

Ground plans - 1500 and present day

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.

SG1

SG2
When this was first built those arches fronted directly on to the river.

woman in period dressSG4

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…

 

IFCA map

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…

Queen Street
The first three pictures were taken on my out from my flat, before we get to stuff from the section between the river and King Street.

Saturday Market PlaceTown HallBPbusFlying gullFerryLower PurfleetYeomanryYeomanry 2HeadgearHelmet plate

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…

TMP2TMP3TMP4Bishop's Lynn HouseSt Ann's HouseSAH1SAH2SAH3St NicholasDoorwaySt Nick's interiorFontCourt in cornerConsistory CourtFancy DressCCGbird and bible 2chandelierBird and biblebird and bible 3OrganwindowPlaqueScreen on seaDann'sLumiere posterStage

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:

Ellipsoid skylight 4
I have never seen a skylight shaped like this – for the moment until I get more information I will call it the Ellipsoid Skylight.

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:

View from the terrace
This is the view looking downriver from the club’s terrace.

THE 101 PROBLEM

In “Anderson Joins the 500 Club and Other Stuff” I included the following problem from brilliant:

SC100 - q

 First of all the answer:

SC100 - a

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:

solution1

The second solution I am sharing here had a particular appeal to me:

solution2

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.