# A roofs is constructed with a pole 10 m high. A spider jumps 2 m and then slips 1 m. In how many times will the spider reach the roof.

2
by srees

2015-04-06T17:24:10+05:30
9 jumps
1jump=(2-1)m
but on the last jump he will be on the top
2015-04-06T17:40:43+05:30

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Height of the pole : 10 m.  jump amount each attempt:  2 m.
slipping amount each time:  1 m.

the jump      height      slipped        final
number       reached    height        position
0m
1                 2m         1m            1 m
2                  3m          1m            2m
:
:
8                 9m            1m            8m
9                 10m

Thus after the 9th attempt/jump, the spider reaches the top of the pole/roof.  Since it goes to the horizontal position, spider does not slip down.
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from the first two attempts/jumps, we see that the spider's final position N meters is equal to the number of jumps N.

we need to find when the spider attains 10 m (target height) - 2 m (jumping height) = 8 meters.  Because, from 8 m  the spider can reach the top and stay there without slipping.

So to attain 8 m (after slipping), it takes 8 attempts.  In the 9th attempt, the spider goes to the top.