please empty your brain below

The tube station word chain comments box.

ยป Potential solutions to the tube word chain by email only, thanks.
<snip>
By email only, thanks.

(also, that's only two stations)

Do Heathrow terminals numbers count for words?
Heathrow stations end in numbers, alas.
Here's my 91 (now trumped by Ali's 92):

Borough, Harrow-on-the-Hill, Lambeth North, Hyde Park Corner, Rickmansworth, Holland Park, Kensington (Olympia), Acton Town, Neasden, North Acton, North Harrow, Westminster, Ruislip Manor, Ruislip, Plaistow, West Harrow, Waterloo, Oxford Circus, Shepherd's Bush, Hatton Cross, Seven Sisters, Southfields, St Paul's, South Ruislip, Pimlico, Oval, Leytonstone, Euston, North Greenwich, Hammersmith, Hornchurch, Hanger Lane, Eastcote, Edgware, Elephant & Castle, Euston Square, East Ham, Marble Arch, Hendon Central, Leicester Square, Epping, Gants Hill, Ladbroke Grove, Edgware Road, Dollis Hill, Liverpool Street, Tooting Bec, Canary Wharf, Fairlop, Pinner, Ruislip Gardens, South Ealing, Great Portland Street, Tottenham Court Road, Debden, Northwood, Dagenham East, Tufnell Park, Kilburn Park, Kew Gardens, South Harrow, West Ruislip, Piccadilly Circus, Stockwell, Leyton, North Ealing, Grange Hill, London Bridge, Elm Park, Knightsbridge, Ealing Common, Northwood Hills, South Kensington, Northfields, Stepney Green, Notting Hill Gate, Earl's Court, Theydon Bois, Southwark, Kennington, Newbury Park, Kilburn, Northwick Park, King's Cross St. Pancras, Swiss Cottage, Embankment, Temple, East Acton, Northolt, Tottenham Hale, Ealing Broadway
Here's Ali's 92 (just trumped by Jerry's 95):

Canary Wharf, Fairlop, Pinner, Ruislip, Pimlico, Oxford Circus, Southfields, Stockwell, Ladbroke Grove, Eastcote, Edgware, Euston, Newbury Park, Knightsbridge, Edgware Road, Debden, Northolt, Tottenham Court Road, Dagenham East, Tottenham Hale, Embankment, Tower Hill, Leicester Square, East Acton, Neasden, Notting Hill Gate, Earl's Court, Turnpike Lane, Elephant & Castle, Ealing Common, Northwood, Dollis Hill, Loughton, Northwick Park, Kilburn, North Ealing, Great Portland Street, Temple, Euston Square, Epping, Grange Hill, Leytonstone, East Ham, Moor Park, Kennington, North Acton, North Greenwich, Hounslow East, Tufnell Park, Kensington Olympia, Arsenal, Lancaster Gate, Elm Park, Kilburn Park, King's Cross St Pancras, Stamford Brook, Kentish Town, Northfields, Shepherd's Bush, Holborn, Northwood Hills, South Ruislip, Plaistow, West Harrow, West Ruislip, Piccadilly Circus, South Ealing, Gants Hill, Lambeth North, Hatton Cross, South Harrow, Westminster, Rickmansworth, Hyde Park Corner, Ruislip Manor, Ravenscourt Park, Kew Gardens, St Paul's, Sudbury Hill, Liverpool Street, Theydon Bois, Seven Sisters, Shepherd's Bush Market, Turnham Green, North Harrow, West Ham, Marble Arch, Hornchurch, High Barnet, Tooting Bec, Clapham Common, North Wembley
Writing some code to solve this problem is quite an interesting challenge. It's a pretty well known problem in Graph Theory (https://en.wikipedia.org/wiki/Longest_path_problem) and it's easy enough to write (or find) some code that will solve the Tube line specific examples.

Solving it for all stations is much harder because the problem is NP-Hard which basically means that as the number of stations increases the size of the problem space increases dramatically. (Someone with a better understanding of the maths can probably explain that better.) The end result is that finding the best solution for larger number of stations is quite tricky.
Here's Jerry's 95 (now trumped by X-P's 97):

Victoria, Aldgate East, Tooting Bec, Canary Wharf, Fairlop, Pimlico, Oxford Circus, Snaresbrook, Kilburn, Notting Hill Gate, Eastcote, Edgware, Elephant & Castle, Euston Square, Epping, Grange Hill, Leytonstone, Edgware Road, Dagenham East, Tottenham Court Road, Dollis Hill, Ladbroke Grove, Elm Park, Kentish Town, Neasden, North Acton, Northfields, Stockwell, Leyton, Northwood, Debden, North Greenwich, Hammersmith, Hornchurch, Hatton Cross, St James's Park, Kensington Olympia, Amersham, Monument, Tower Hill, Lambeth North, Holland Park, Kilburn Park, Knightsbridge, East Ham, Maida Vale, Ealing Common, Newbury Park, Kensal Green, Northwick Park, Kennington, North Ealing, Gants Hill, Lancaster Gate, East Acton, Northolt, Theydon Bois, South Kenton, Northwood Hills, Sloane Square, Euston, North Harrow, Westminster, Rickmansworth, Hendon Central, Leicester Square, Earl's Court, Temple, Embankment, Tufnell Park, Kew Gardens, South Ealing, Green Park, King's Cross St Pancras, Shepherd's Bush, Hyde Park Corner, Ruislip Manor, Ruislip, Piccadilly Circus, South Ruislip, Plaistow, West Ruislip, Pinner, Ruislip Gardens, St. Paul's, Seven Sisters, Southfields, South Harrow, West Harrow, West Ham, Marble Arch, Harrow-on-the-Hill, Liverpool Street, Tottenham Hale, Ealing Broadway
In X-P's 97 I've replaced
Clapham South, Hendon Central, Lancaster Gate
with
Canary Wharf, Fairlop, Piccadilly Circus, Sloane Square
to make 98.

What I can't do is squeeze in Hendon Central and Lancaster Gate somewhere else to make the magic 100.
I'm currently trying to work out the upper limit on chain length by considering how many stations are going to be 'wasted' (e.g. stations that can only appear at the start or finish of a chain). I've managed to get the limit down to just 107 although I think it can go lower.
Here's the previous record of 98, now beaten by X-P's 99:

Bromley-by-Bow, West Harrow, West Ruislip, Pimlico, Oxford Circus, Sudbury Hill, Liverpool Street, Temple, Edgware, Euston, Neasden, North Harrow, Waterloo, Oval, Ladbroke Grove, Eastcote, East Ham, Marble Arch, Hammersmith, Hatton Cross, Seven Sisters, South Harrow, Westminster, Ruislip Manor, Ruislip, Pinner, Ruislip Gardens, St. Paul's, Shepherd's Bush, Hornchurch, Hainault, Tottenham Hale, Euston Square, Elm Park, Kilburn Park, Kew Gardens, Shepherd's Bush Market, Tooting Bec, Canary Wharf, Fairlop, Piccadilly Circus, Sloane Square, Elephant & Castle, Epping, Gants Hill, Leyton, Northwood Hills, South Ruislip, Plaistow, West Ham, Monument, Theydon Bois, Stockwell, Leicester Square, East Acton, North Acton, North Greenwich, Hyde Park Corner, Rickmansworth, Holland Park, King's Cross St Pancras, South Ealing, Grange Hill, Lambeth North, High Barnet, Totteridge & Whetstone, Ealing Common, Northfields, Southfields, St James's Park, Kensington (Olympia), Amersham, Mill Hill East, Tower Hill, Leytonstone, Earl's Court, Tufnell Park, Kensal Green, North Ealing, Green Park, Knightsbridge, Embankment, Turnham Green, Notting Hill Gate, Edgware Road, Dollis Hill, Loughton, Newbury Park, Kenton, Northolt, Tottenham Court Road, Debden, Northwick Park, Kennington, Northwood, Dagenham East, Turnpike Lane, Ealing Broadway










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