Mr Broadwith
4.1K posts

Mr Broadwith
@24HourMaths
Maths is life. #85. #170
Somewhere near Watford Katılım Ekim 2011
400 Takip Edilen2.4K Takipçiler

@24HourMaths s = t²
r = s² = t⁴
AD² = AB²
(t – s)² + (s – r)² = 2(s – r)²
t – s = s – r
t – t² = t² – t⁴
t⁴ – 2t² + t = 0
t(t – 1)(t² + t – 1) = 0
Solve for t in (0,1):
t = (√5 – 1)/2
t² = (3 – √5)/2
t⁴ = (7 – 3√5)/2
t² – t⁴ = √5 – 2
AB² = 2(s – r)² = 2(t² – t⁴)² = 18 – 8√5

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@24HourMaths Went through it more methodically, found 4 more.
1, 2, 5, 7
1, 3, 4, 5
1, 3, 4, 6
1, 3, 5, 6
I believe this is now every combination
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@FO6DC4 I do not think that that is a complete solution set, but your answers are all correct.
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@24HourMaths If I've understood the question correctly, then I think I have 4.
1, 2, 3, 7
1, 2, 4, 5
1, 2, 5, 8
1, 3, 4, 9
I don't believe there are any others
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@grundbirn This is correct - there was a typo in the question... the first x shouldn't be there! then it is a smoother answer :)
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Route being followed by Pete Dyson:
ridewithgps.com/routes/50155896
He is proactively avoiding the A1 - adding around five miles to the 2021 route.

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Pete Dyson (Bath CC) going for the RRA London to Edinburgh record today. Nice day for it!
Road Records Association@RRA_GB
Today at 0500 Pete Dyson (Bath CC) set off from the Rowland Hill statue, King Edward Street, London. He is attempting to break the RRA London to Edinburgh record set in 2021 by Michael Broadwith. Current record: 17.42.47 Tracking link live.garmin.com/session/1a8343…
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