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What a day-size cap really costs — and it is not what you would guess.

The 214 in the Fewest Walks

There is a trick to this question, and it is worth getting out of the way first: with no limit on the size of a day, the answer is one walk. We have already published it — the perfect round visits all 214 in a single continuous line. So “the fewest walks” is never a fact on its own. It is a function of how big a day you are willing to have, and the useful question is what a smaller day costs you.

We solved that, sixteen ways. Each combination of a distance cap and an ascent cap gets its own answer: the smallest number of separate walks that reaches every Wainwright it can reach, from 217 start points a person has actually verified. 15 of the 16 car-mode answers are proven minimums rather than good attempts — the solver reports a matching lower bound, so nothing smaller exists.

The curve, and the thing it would hide

What a day-size cap costs - and what it leaves behind020406080100WALKS REQUIRED8298939310 km8515/20/25 km alike85655915 km8620/25 km alike544020 km533925 kmFELLS REACHABLEall 214−98−41−34−34−93−19−2−2−93−15−93−15600 m900 m1200 m1500 mASCENT CAP PER DAY · each line is a distance capcovers all 214 — comparableincomplete — a lower number here means fewer FELLS, not fewer walks

Walks required above; fells actually reachable below, on the same axis. The two must be read together — see the note.

Why the gentle days look cheap, and are not. Read the top panel alone and a 10 km / 600 m day looks like a bargain: the fewest walks on the chart. It is not a bargain, it is an incomplete answer — on days that size only 116 of the 214 can be reached at all, and the remaining 98 are not conquered but uncounted. Those points are drawn hollow. Only the filled ones are answering the same question as each other.

Three things the solve found

Gentle days do not finish the round

98 of the 214 cannot be reached at all on 10 km / 600 m days, there and back from a start point. Not “hard” — unreachable within that budget.

Ascent binds. Distance is slack

39 walks is the fewest that still finishes all 214, on 25 km / 1500 m days. Loosening the distance cap barely moves the answer: at 600 m of ascent the 15 / 20 / 25 km caps all land on 85; at 900 m of ascent the 20 / 25 km caps all land on 86.

Linear walks barely help

0–2 walks saved by allowing a walk to finish somewhere else on the same bus route — and nothing at all at 4 of the 16 caps. Only 23 of the 217 start points have a bus service, which is the whole explanation.

All sixteen answers

Distance capAscent capWalks With busesFells reachedResult
10 km600 m8280116 −98proven
10 km900 m9897173 −41proven
10 km1200 m9392180 −34proven
10 km1500 m9392180 −34proven
15 km600 m8583121 −93proven
15 km900 m8585195 −19proven
15 km1200 m6564212 −2proven
15 km1500 m5958212 −2proven
20 km600 m8583121 −93proven
20 km900 m8686199 −15proven
20 km1200 m5452214proven
20 km1500 m4040214proven
25 km600 m8583121 −93proven
25 km900 m8686199 −15proven
25 km1200 m5351214proven
25 km1500 m3937214best found

Rows in grey do not reach all 214; their walk count is not comparable with the rest. “Proven” means the solver also produced a matching lower bound.

Are they walks anyone would actually choose? Partly. In a blind sample of 92 of these computed days, the author would not recommend about 35% of them as they stand — usually because the day is simply large, which is what a generous cap buys, or because the start point is a long way from the first summit. That does not change the count: the minimum is a property of the caps and the map, not of how pleasant the resulting day is. It is the difference between how few are possible and which ones to walk, and only the first question is answered here.

What a person did, for comparison

Stuart Marshall's Walking the Wainwrights (2000) sets out a round of the 214 in 36 circular walks — and he walked them. This page did not. A solver proposing 39 lines is not a better answer than his 36: his day sizes are his own, ours are caps we chose, and a smaller number bought with bigger days is not an achievement. His book is the reason to treat the numbers here as arithmetic rather than advice.

How it was worked out

Solved 2026-08-11 · 32 scenarios · data: index.json