spoiler alert – for the question, see yesterday’s post before reading on!
The answer is 382.
I just cannot transcribe Mr Hill’s diagram in a shape that reflects the MS, but it says:
382 halved is 191
and one more
Rest (i.e. left) 190 after the first gate
2nd gate: 190 halved is 95, and one more to the porter leaves –
3rd gate: 94 halved is 47, and one more –
4th gate: 46 halved is 23, and one more –
5th gate 22 halved is 11, and one more –
6th gate 10 halved is 5, and one more –
7th gate 4 halved is 2, and one more –
‘and at last one he bare away.’
More little conundrums from a 16th century London grocer another day!
From Balliol’s MS 354, the commonplace book of Richard Hill, a London Grocer in the first half of the 16th century, a medieval riddle, or rather an arithmetic word-problem of the kind we used to get a lot of in school. Plus ça change…
Ther was a man went in to an orchard & toke
sertayn apples //and he must pass vij gattes
and ye porter of ye first gate will not latt hym passe
except he geve hym half his aples & on mo
& so he gave hym / and than he commeth to ye ijde
gate & ye porter toke from hym half his apples yat he hade left &
i mo / and so seruid hym ye iijde portter / & ye iiijth
portter & vth & vjth & vijth porter / So at ye laste
he bare but on apple a way // how many
apples had he at the first /
There was a man who went into an orchard and took a certain number of apples. On his way out he had to pass through seven gates: the porter at the first gate would not let him pass unless he give him half his apples plus one more, and he did so. And then he came to the second gate, and that porter took from him half the apples that he had left, plus one more, and the third, fourth, fifth, sixth and seventh porters did the same. So in the end he carried only one apple away. How many apples did he start with?
Answer (from the manuscript) tomorrow!