Question 160158
goes up 3 in the day and goes down 2 in the night.
at the end of the first day there's a gain of 3.
at the end of each succeeding day there's a gain of 1 (loss of 2 during the night).
end of day 1 he's up 3
end of day 2 he's up 4
end of day 3 he's up 5
end of day 7 he's up 9
end of day 8 he's up 10
you're correct.
number of days is 8.
now the formula.
let x be the number of days needed to get out of the well.
formula looks like it will be
(x-1)*(3-2) + 3 = 10
what this says is that you have x-1 days where the net gain was only 1.
that would be the loss of 2 the night before plus the gain of 3 during the day.
the + 3 means you got a net gain of 3 the first day.
so (x-1)*(3-2) + 3 = 10
solving you get
(x-1)(1) + 3 = 10
x - 1 + 3 = 10
x - 1 = 7
x = 8
i must admit i didn't think about it correctly the first time i looked at it.
congratulations on good logic.