Number of ways to get a nine-dart finish

Off-topic post.

Just as I am gearing to watch the wonder that is the 2018 World Darts, I noticed this puzzle on 538

“In competitive darts, a player starts with 501 points and subtracts the score of each throw. He or she must finish with exactly zero points. (Also, per the rules, the final dart must land in either the bullseye or the outer, doubled segments.) What is the minimum number of throws? How many different ways are there to do it?”

The first part is very easy – the maximum with any one dart is 60 points. Therefore the maximum with eight darts is 480 points, so you can’t score 501 in eight darts or fewer. The combination T20, T20, T20, T20, T20, T20, T20, T19, D12 shows it can be done in nine darts, so this is the minimum. But how many ways are there?

We know the last dart must be a double or bullseye. Call this last value D. Then the first 8 darts must equal 501-D. As above the first 8 darts are worth at most 480 points, so 501 – D <= 480. I.e. D >= 21. Thus the possible  ninth darts are:

[Bull, D20, D19, D18, D17, D16, D15, D14, D13, D12, D11]

So for each of these last darts, we must find how the number of combinations of the first 8 darts give the right score and then add these up to get the total number of combinations.

To prune the search space, note the least possible value of the eight darts is 501-50 = 451 and the most possible value of seven darts is 7*60=420, so at the absolute least each of the first eight dart must be worth at least 451-420=31 points. There is no way to get 31 points (31 is prime) so in fact every dart must be worth 32 points. This leaves the following set of possible darts to consider for the first eight darts:

C = [T20, T19, T18, T17, Bull, T16, T15, T14, D20, T13, D19, D18, T12, D17, T11, D16]

Noting that C is descending numerical order, my recursive algorithm was as follows:

  • Maintain an index into this “consideration array”, C
  • Maintain a remaining target T and remaining number of darts R
  • Maintain a stack starting empty
  • T starts at 501-D and R starts at 8
  • The next value is C[i].
    • if R == 1 and T == C[i] we have found a solution and the stack consists of the darts we need (plus the ninth dart recorded separately)
  • Otherwise If T- C[i] > 0 and R >= 2, then C[i] is potentially part of the solutoin for the current stack, so recurse with T -> T-C[i], R -> R-1, i staying the same, and append C[i] to the stack
  • Otherwise if i < 8 and if C[i+1] * R >= target (i.e. the remaining numbers are big enough to potentially reach the target – this bit relying on the ordering of C), then recurse with T -> T, R->R, i -> i+1 and keeping the same stack.

The algorithm starts with T = 501-D, R=8, i=0 and the stack empty.

Running the algorithm, this way we get all possible solutions, not accounting for re-ordering. Naively there are 8! = 5040 different ways to re-order 8 darts, but if the same dart appears k times in the solution, then the same solution is appearing k! times in this set. In fact each solution can be ordered in  8 Choose{k_1,…k_r} ways where k_i is the number of times a particular dart appears in the solution (i.e. this is just the usual multinomial coefficient formula for counting re-arrangements).

I was taken aback by just quickly these recursive algorithm ran when implemented as a simple Python program. Here are the results:

[T20, T20, T20, T20, T20, T20, T19, D17] , BUL (56 ways)
[T20, T20, T20, T20, T20, T20, T17, D20] , BUL (56 ways)
[T20, T20, T20, T20, T20, T19, T18, D20] , BUL (336 ways)
[T20, T20, T20, T20, T20, T17, BUL, BUL] , BUL (168 ways)
[T20, T20, T20, T20, T19, T19, T19, D20] , BUL (280 ways)
[T20, T20, T20, T20, T19, T18, BUL, BUL] , BUL (840 ways)
[T20, T20, T20, T19, T19, T19, BUL, BUL] , BUL (560 ways)
[T20, T20, T20, T20, T20, T20, T17, BUL] , D20 (56 ways)
[T20, T20, T20, T20, T20, T19, T18, BUL] , D20 (336 ways)
[T20, T20, T20, T20, T19, T19, T19, BUL] , D20 (280 ways)
[T20, T20, T20, T20, T20, T20, T20, T15] , D18 (8 ways)
[T20, T20, T20, T20, T20, T20, T19, T16] , D18 (56 ways)
[T20, T20, T20, T20, T20, T20, T18, T17] , D18 (56 ways)
[T20, T20, T20, T20, T20, T19, T19, T17] , D18 (168 ways)
[T20, T20, T20, T20, T20, T19, T18, T18] , D18 (168 ways)
[T20, T20, T20, T20, T19, T19, T19, T18] , D18 (280 ways)
[T20, T20, T20, T19, T19, T19, T19, T19] , D18 (56 ways)
[T20, T20, T20, T20, T20, T20, T19, BUL] , D17 (56 ways)
[T20, T20, T20, T20, T20, T20, T20, T17] , D15 (8 ways)
[T20, T20, T20, T20, T20, T20, T19, T18] , D15 (56 ways)
[T20, T20, T20, T20, T20, T19, T19, T19] , D15 (56 ways)
[T20, T20, T20, T20, T20, T20, T20, T19] , D12 (8 ways)

Adding them up, there are a grand total of 3944 ways to do a nine-darter… even Phil Taylor hasn’t done all of those!

 

 

 

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CS9 Chiswick debate – my review

 

Yesterday (Tuesday 17th) I attended a public consultation meeting on CS9. This was the first time I have ever attended a TfL consultation, so thought I would write up my thoughts.

First up, thank you to ChiswickCalendar for organizing this. They did a good job – the Boston Room at George IV was a good venue and the recording was a nice touch. They also got together a good mix of contributors – on stage we had Will Norman the TfL champion for walking and cycling, a pro-scheme Chiswick resident, an anti-scheme Chiswick resident and a local business owner with concerns about the scheme. Off stage there were numerous technical people from TfL, council representatives and councillors, more local business people and someone from (I think) the Hounslow Cycling Campaign. The debate was chaired by Julian Worricker – a BBC News presenter and Chiswick resident. He made sure that a significant number of people across the floor got the chance to make points.

CS9_debate

The debate was well-attended

I thought Will Norman and the TfL team did well. At the beginning Norman painted the Mayor’s big picture strategy and why we need more “active transport” (the usual reasons – population growth, inactivity crisis pollution) and in particular why the proposed route for CS9 is a good one (e.g. 3,000 daily cyclists along the Chiswick High Road already). NB someone else said the DfT figures are a mere 2,000 daily users. Norman delegated to the TfL for technical details at the right times – e.g. for issues about modelling, about loading bays, pavement widths etc. These women and men seemed on top of their brief and generally refuted some of the objections that some had to the room.

I estimate the balance of the room was roughly 75% “anti-scheme” and roughly 25% pro-scheme – estimated from clap volume when someone made a point!

The debate was almost entirely centred around the Chiswick High Road – there was virtually no discussion about the “downstream” end around Kew Bridge and Brentford or upstream around Hammersmith. One pro-cyclist did voice my primary concern about the scheme ending at Olympia and not Hyde Park. If the scheme goes ahead, there will be more cyclists mixing it with the traffic on the highly dangerous Kensington High Street.

Interestingly we heard very little objection to the scheme from a motoring perspective. If people were concerned that this scheme would actually =increase= pollution because of increased congestion, for example, this was not voiced. Those against were much more concerned about the loss of pavement than loss of road (both occur in the scheme but there is much more road loss than pavement). Early on someone did say “this scheme will fracture the community” – a close echo of the “loss of cafe culture” that we have heard about in social media and on the web. This objection was a bit annoying to me – it is almost meaningless (how =does= one fracture an abstract noun?) so it is hard to debate with. Much better to look at the facts – five of the six restaurants with seating outside will see NO reduction in pavement size. The remaining restaurant (Byron) will have room for exactly the same number of seats, as well as pavement wide enough for two wheelchairs to pass each other. There will also be a net gain in number of trees on the High Road. Side roads will become easier to cross and the existing crossings will all be retained and in some cases made wider. Ok, so some cars will be replaced by bikes – but as far as I can this only diminishes the community if you are fervently anti-cycling!

And, oh yes, there were numerous folk present who really just didn’t like cyclists. In naivety I previously thought this people existed only on the Daily Mail comment pages, so it was fascinating, in a way, to hear these thoughts made flesh: “Only a few months ago I had to jump out of the way of one on the pavement!”.. “They all jump red lights”… “They all wear lycra and will break a 20mph speed limit”. A number of times we heard cyclists being treated as a single homogeneous group – all to blame for each others ills. In fact I came away with the conclusion that some people don’t want a protected cycle lane as a form of spite or punishment – yes the roads are dangerous but they deserve it?! I am tempted to start treating all motorists as a block too.

CS9_debate_beer

Some of the comments about cyclists turned me to drink.

The Wellesley Road ratrun received some attention. This was criticised on two sides – a number of the pro-scheme people present pointed out that it means that the protected lane will not run to Chiswick Park, a significiant employment base in the area. Others pointed out that by closing the outlets on to the South Circular, journey times for people living in that area will increase when they are heading out of town to the south or west. That’s true, but unfortunately the obvious counterpoint – that removing all the rat-running will cut traffic by 80% and make the streets a much nicer place to live, was not made clear enough, in my opinion.

There was quite a lot of “well of course I support the idea of a cycle lane, just not here, oh no!”. In particular quite a few people thought the scheme should go along the A4. There wasn’t a precise proposal so I don’t know if they intended the flyover to be used, or how people would get up to it from Brentford or Kew Bridge. TfL and the council did point out that they had considered the idea as unworkable, but also people should be careful what they wish for as making the A4 less attractive for traffic would push more traffic down the High Road… how about that for “fracturing a community”?

Towards the end we heard from a member of the Our Lady of Grace Catholic Church, which has infamously asked its parishoners to pray for CS9 to be moved elsewhere. It is undoubtedly unfortunate that due to tree positions that at this very western end of the cycle track’s route down the High Road, the track is set to take space from the pavement when it should be the road. Even removing a tree may be an option here – I am sure TfL will be looking at options around this when the consultation closes. BUT, when listing to the guy’s “health and safety” comments, I was really struck by how health and safety really has gone mad when considering the scheme. During the evening and in recent weeks we heard

  • Concerns about the delivery drivers having to push their trollies a tiny bit further when making deliveries, causing “health and safety” issues.
  • Concerns that if the church caught fire and had to be evacuated, then people would have to walk a little further down the pavement to escape it than they would today.
  • Concerns that a bride might trip over in her wedding dress if the route to the altar was made more complex.

WHY is it that those anti the scheme are able to take these concerns so seriously, but don’t seem to take serious the massively more significant danger of 3,000 daily cyclists being passed close and fast by multi-ton cars, trucks and buses. There have been more than 80 accidents on this road in recent years – this is where our REAL concerns should lie. So yes, I am sure tweaks can be made, but CS9 surely MUST go ahead.

The consultation closes at the end of October and can be accessed at https://consultations.tfl.gov.uk/roads/cs9/?cid=cs9

 

 

 

 

 

 

Cycle safety review

On 21st September 2017, the government launched an “urgent review into cycle safety” following the tragic death of a pedestrian who had been ridden into by a cyclist riding a track bike with no front brake.

The first sentence of the review says “following a series of high profile incidents” and the Transport Minister Jesse Norman is quoted as saying “given recent cases, it is only right..”.

There has only been one recent high profile case.

The review will be in two phases. Phase one will “analyse the case for creating a new offence equivalent to causing death or serious injury by careless or dangerous driving to help protect both cyclists and pedestrians.” It is unclear how bringing in new laws against them will “protect cyclists”!

The second phase will “be a wider consultation on road safety issues relating to cycling […] and will consider different ways in which safety can be further improved between cyclists, pedestrians and motorists.”

Laura Laker response in The Guardian – “Minister’s call for cyclists to behave is more headline-grabbing hypocrisy

Norman’s response to that article (also in The Guardian): We want to make our roads safer for everyone – especially cyclists

Of course Norman’s response ignores Laker’s central point, which is that the DfT continues to ignore the demands to carry out the promised review of 2014 of all road sentencing, but one cyclist case that generates tabloid headlines is enough to trigger an urgent review. Why is this hypocrisy?… because Norman himself urged us to avoid rushes to judgement when celebrating Edmund Burke in an FT OpEd.

It seems a given that a new cycling law will be brought in, even though the cyclist in the track bike case didn’t actually receive the maximum sentence for the “wanton and furious cycling” offence he was guilty of.

Where the real battle begins is “phase two”. Given that Norman wrote to all cycling organisations asking them to tell how cyclists how to behave, it is clear that he doesn’t treat them equally with motorists, however much of a “keen cyclist” he may be. Can you imagine a transport minister writing to the AA, RAC, Road Haulage Association etc, every time a car-related death occurred (which is about 5 times a day)?

So what might Norman have in mind.. well here are at least five times , a transport minister has been pressed in Parliament to introduce a mandatory cycle helmet (and the first link shows the pressure has been there for decades). Let’s hope they don’t propose both helmets and hi-viz and then water it down to just one of those (in the spirit of “compromise”). Such clear victim-blaming and piling on of the out-group will discourage cycling further, making it all the more dangerous for those left, despite the obvious pro-health and anti-pollution benefits that MORE cycling would bring.

 

 

 

Project Thames Crossings

As a side-project to my squares project, I’m also keeping track of which Thames crossings I’ve “done”.

I’ve chopped things up into the following categories:

  • Road/bridges tunnels navigable by bike: I must’ve ridden across/ for them to “count”. Example: Waterloo Bridge.
  • Foot bridges and tunnels: I must’ve ridden or wheeled my bike across/through these for them to count. Example: Greenwich Foot Tunnel.
  • Railway bridges and tunnels: I’m counting these if I’ve been on the relevant train/tube/DLR line – the bike doesn’t have to have come with me. Example: Kingston Railway Bridge
  • Ferries: If the ferry allows bikes to come on board (and most do) then the bike must come for it to count. Example: Hammerton’s Ferry.
  • Roads inaccessible to bike: If the road has some custom arrangement for bikes (e.g. Dartford crossing), I must use that custom arrangement. Otherwise any type of crossing will count. Example: M3 Bridge at Chertsey.
  • Other. One in this case – Emirates “Air Line” Cable car. I did not take the bike when I went on this, but I believe you can.

Within each category, crossings are listed in most-downstream order first. Links in the first column lead to a Wikipedia page or similar resource. Links in the third column lead to a Strava activity where I “ticked” the crossing.

Road bridges / tunnels navigable by bike (58/74 crossed)

Rotherhithe Tunnel Road tunnel DONE
Tower Bridge Road bridge DONE
London Bridge Road bridge DONE
Southwark Bridge Road bridge DONE
Blackfriars road bridge Road bridge DONE
Waterloo Bridge Road bridge DONE
Westminster Bridge Road bridge DONE
Lambeth Bridge Road bridge DONE
Vauxhall Bridge Road bridge DONE
Chelsea Bridge Road bridge DONE
Albert Bridge Road bridge DONE
Battersea Bridge Road bridge DONE
Wandsworth Bridge Road bridge DONE
Putney Bridge Road bridge DONE
Hammersmith Bridge Road bridge DONE
Chiswick Bridge / A316 Road bridge DONE
Kew Bridge Road bridge DONE
Twickenham Bridge Road bridge DONE
Richmond Bridge Road bridge DONE
Kingston Bridge Road bridge DONE
Hampton Court Bridge Road bridge DONE
Walton Bridge Road bridge DONE
Chertsey Bridge Road bridge DONE
Staines Bridge Road bridge DONE
M25 / A30 Runnymede Bridge Road bridge DONE
Albert Bridge (Datchet) Road bridge DONE
Victoria Bridge (Datchet) Road bridge DONE
Windsor Bridge Road bridge DONE
Queen Elizabeth Windsor Bridge Road bridge DONE
Maidenhead Bridge Road bridge DONE
Cookham Bridge Road bridge DONE
Marlow bypass / A404 bridge Road bridge TODO
Marlow Bridge Road bridge DONE
Henley Bridge Road bridge DONE
Sonning Bridge Road bridge DONE
Reading Bridge Road bridge DONE
Caversham Bridge Road bridge DONE
Whitchurch Bridge (Pangbourne) Road bridge TODO
Goring and Streatley Bridge Road bridge DONE
Winterbrook Bridge (A4130 / Wallingford Bridge) Road bridge DONE
Wallingford Bridge Road bridge DONE
Shillingford Bridge Road bridge DONE
Clifton Hampden Bridge Road bridge DONE
Sutton Bridge Road bridge TODO
Abingdon Bridge Road bridge DONE
Isis Bridge (A423 Oxford Ring Road) Road bridge DONE
Donnington Bridge Road bridge DONE
Folly Bridge Road bridge DONE
Osney Bridge Road bridge DONE
Godstow Bridge Road bridge TODO
Thames Bridge / A34 Road Bridge Road bridge TODO
Swinford Toll Bridge Road bridge DONE
Newbridge Road bridge DONE
Tadpool Bridge Road bridge TODO
Radcot Bridge Road bridge TODO
St John’s Bridge, Lechlade Road bridge DONE
Halfpenny Bridge Road bridge TODO
Hannington Bridge Road bridge TODO
Castle Eaton Bridge Road bridge TODO
A419 Road Bridge (Cricklade bypass) Road bridge DONE
Cricklade Town Bridge Road bridge DONE
Bridge at Waterhay Road bridge DONE
Bridge on High Road, Ashton Keynes Road bridge DONE
Bridge on The Derry, Ashton Keynes Road bridge DONE
Bridge on Gosditch, Ashton Keynes Road bridge DONE
Bridge on Church Walk, Ashton Keynes Road bridge DONE
Bridge on B4696, Ashton Keynes Road bridge TODO
Bridges on Mill Lake Walk x4 Road bridge TODO
Bridge on Oaksey Road (aka Spine Road W) Road bridge TODO
Neigh Bridge Road bridge TODO
Bridge south of Ewen Road bridge TODO
Bridge west of Ewen (Parker’s Bridge) Road bridge DONE
A429 Bridge North of Kemble Road bridge TODO
A433 Bridge Road Road bridge DONE

Footbridges and tunnels

Woolwich foot tunnel Foot tunnel TODO
Greenwich foot tunnel Foot tunnel TODO
Millennium Bridge (“Wobbly bridge”) Foot bridge DONE
Hungerford Bridge Rail / foot bridge DONE
Barnes Railway Bridge Rail / foot bridge DONE
Richmond Lock and Footbridge Foot bridge TODO
Teddington Lock Footbridge Footbridge DONE
Summerleaze Footbridge Foot bridge TODO
Bourne End Railway Bridge Rail / foot bridge TODO
Temple Footbridge Foot bridge TODO
Hambleden Lock Foot bridge TODO
Caversham Lock Foot bridge TODO
Christchurch Bridge (opened 2015) Foot bridge TODO
Benson Lock Footbridge TODO
Little Wittenham Bridge Foot bridge TODO
Day’s Lock bridge Foot bridge TODO
Sutton Pools footbridges Foot bridge TODO
Culham Lock footbridge Foot bridge TODO
Abingdon Lock bridge Foot bridge TODO
Sandford Lock bridge Foot bridge TODO
Iffley Lock Foot bridge TODO
Grandpont Bridge, Oxford Foot bridge TODO
Gasworks Bridge, Oxford Foot bridge TODO
Medley Footbridge Foot bridge TODO
Pinkhill Lock Foot bridge TODO
Hart’s Weir Footbridge Foot bridge TODO
Duxford Ford and Shifford Lock Cut Foot bridge TODO
Tenfoot Bridge Foot bridge TODO
Rushey Lock Foot bridge TODO
Old Man’s Bridge Foot bridge TODO
Eaton Footbridge Foot bridge TODO
Buscot Lock Foot bridge TODO
Bloomers Hole Footbridge Foot bridge TODO
Water Eaton House Bridge Foot bridge TODO
Eysey Footbridge Foot bridge TODO

Railway bridges and tunnels

High Speed 1 tunnels Rail DONE
DLR / Woolwich Arsenal DLR TODO
Jubilee Line (Canary Wharf -> North Greenwich) Tube DONE
DLR / Cutty Sark DLR DONE
Jubilee Line (Canada Water -> Canary Wharf) Tube DONE
Thames Tunnel (London Overground: Rotherhithe to Wapping) London overground DONE
Northern Line (City Branch) Tube DONE
Cannon Street rail bridge Rail DONE
Blackfriars rail bridge Rail DONE
Waterloo and City Line tunnel Tube DONE
Northern Line (Charing Cross Branch) Tube DONE
Bakerloo Line Tube DONE
Jubilee Line Tube DONE
Victoria Line Tube DONE
Victoria rail bridge / Grosvenor Bridge Rail DONE
Battersea Rail Bridge (London Overground) London overground DONE
Fulham Railway Bridge (District Line to Wimbledon) Tube TODO
Kew Railway Bridge (Overground/Underground to Richmond) Tube / overground DONE
Richmond Railway Bridge Rail DONE
Kingston Rail Bridge Rail TODO
Staines Railway Bridge Rail DONE
Black Potts Railway Bridge (into W&E Riverside) Rail DONE
Windsor Railway Bridge (into W&E Central) Rail TODO
Maidenhead Railway Bridge (GWR mainline) Rail DONE
Shiplake Railway Bridge (Henley branch line) Rail TODO
Gatehampton Railway Bridge (GWR mainline) Rail DONE
Moulsford Railway Bridge (GWR mainline) Rail DONE
Appleford Railway Bridge (Cherwell Valley line – Reading to Oxford) Rail DONE
Nuneham Railway Bridge (Cherwell Valley line – Reading to Oxford) Rail DONE
Kennington Railway Bridge (Cowley branch line) Rail TODO
Osney Railway Bridge (Cherwell Valley Line – Reading to Oxford) Rail DONE

Ferries

Gravesend-Tilbury ferry Ferry TODO
Woolwich ferry Ferry DONE
Canary Wharf / Rotherhithe Ferry Ferry TODO
Hammerton’s Ferry Ferry TODO
Hampton Ferry Ferry TODO
Shepperton to Weybridge Ferry Ferry TODO

Roads inaccessible to bikes

Dartford crossing southbound No bikes road bridge TODO
Dartford crossing northbound No bikes road tunnel TODO
Blackwall Tunnel southbound No bikes road tunnel TODO
Blackwall Tunnel northbound No bikes road tunnel TODO
M3 Chertsey Bridge Road bridge (motorway) DONE
M4 bridge at Maidenhead Road bridge (motorway) DONE

Other

Emirates Air Line Cable car DONE

Clumps are now clusters

After a very active discussion on the Ride Every Tile Strava club (first one I’ve seen with 100 comments actually), it is great to see we have a solution to the “impossible-to-visit squares” problem. And that solution is “max cluster”. The idea of a maximum cluster is very similar to the idea of “max clump” described earlier on this blog . In fact the algorithm is the same, it is just the name that has improved. Although I am biased because I played a role in their creation, I do think clumps are a reasonable solution to the impossible squares problem because

  • No matter how many impossible squares you have, you can join the max clump game. In the worst case you pay a “fine” of 5 points for not visiting a square, and if there are a number of unvisitables next to each other, the cost per square works out less than 5.
  • The cluster metric adapts to whatever topology is in your area. If there’s a coastline that does go north/south or east/west, you can make a pretty pattern by visiting everywhere along the coasts.
  • The max square score is a very slow-growing score (like Eddington number it grows with the square root of effort) so it requires long-term patience to increase. The max cluster on the other hand brings more instant gratification.
  • Even if max square is working out nicely for you, it is still another thing to look at VeloViewer.
  • As a bonus, the map UI in VeloViewer has become much more sophisticated (details at Ben’s post here). Amongst other things, you can see cluster and visited-squares colour the same if you want to, recovering the old UI.

cluster_prod

Using the new flexible UI to show the damage the Squarpocalypse has done!

A further bonus is that some of Ben’s legions of followers on Twitter/Facebook have been attracted Ride Every Tile, and we now have over 180 members (from about 40 two weeks ago). And with that influx, there’s been some great new ideas. In particular “Half-Fast” Mike who rides in and around Tokyo has shared a great idea for getting squares to be displayed on your Garmin Edge as you are out and about – increasing the chances that you will actually bag all the squares you hope to bag on a ride – full details here

Finally, the race to recover lost squares following the Squarpocalypse has heated up. I dragged myself out of bed (again) to do a very similar route to the last time I dragged myself out of bed (ride report here for that one ) except this time I would bag the four squares that I had missed. Despite leaving home 12 minutes later than target (4.42am) I reached work at 8.04am, four minutes later than target – traffic lights aren’t always more red than you think they ought to be. This got me back to 32×32. At the time of writing this actually third on the leaderboard, but the situation is very fluid.

As always, there was something unexpectedly pretty or interesting on a squares ride… I had to loop round the South Mimms services to bag a square just outside Potters Bar. Service stations are normally pretty awful places (Sartre wasn’t talking about services when he said “L’enfer, c’est les autres” but the phrase always comes to mind) and South Mimms, at the junction of the M1 and M25 is pretty typical so it was lovely to discover that the village of South Mymms has many centuries of history and a church that dates to 1136. As usual I regret not stopping to get photos – some at http://stgiles-stmargarets.co.uk/st-giles-history

Strava link for the ride: https://www.strava.com/activities/1045242141

 

 

 

 

Clump examples

[19th June 2017: Updated to add: Ben VeloViewer has now done a better proof-of-concept – check out your own VeloViewer map  for an example! Also see Ben’s Facebook post for more details and for your chance to vote on the name for this new thing. At the moment it looks like “cluster” will win out over “clump”.]

The pictures below show some example “max clumps” for real data. The “max clumps” shown here are calculated using the following rules:

  •  A square is in a clump if
    • You have visited it
    • You have visited all four squares that are adjacent to that square.
  • If two adjacent squares are both in a clump they are in the “same clump”
  • Divide up all your visited squares into clumps. The clump with the most squares in it is called the max clump.

These rules are not set in stone or sent by God or anything else that. They are just some choices that seem to create some nice patterns.

(more commentary follows below the pictures)

clump_pete_bartlett

My max clump

clump_eric_nichols

The max clump of the rider who was North American leader before “Squarepocalypse”

clump_phill_cloke

The max clump of the rider who was UK leader before “Squarepocalypse”

I quite like the middle map – it clearly shows that the cyclist in question has really been up and down everywhere on the New England coast.

All three maps feature lots of cross shapes. These are due to me generating the data in the days immediately after the squarepocalypse. If there is a missing square then not only is that square missing from your clump, but also the four squares adjacent to it aren’t included either This has the effect that a missing square has slightly multiplied effect on your “clump score” – meaning that you should still try hard to visit every square. But if there are truly unreachable squares, then you aren’t crippled from playing the squares game – you just get a 5 point penalty effectively.

Feedback welcome at the Ride Every Tile Strava club .