That tells us that the ladder has an ODD number of rungs, because if it had
an EVEN number of rungs, there would be no middle rung.

Suppose she started on rung N. Then there were N-1 rungs below her, and
N-1 rungs above her.  So altogether on the ladder there are 2(N-1) rungs
plus the 1 middle rung, or 2(N-1)+1 which simplifies to 2N-2+1 or 2N-1
rungs on the ladder.  

So she started on the middle rung, which is rung N. 

Then she was on rung N+2

Then she was on rung N+2 - 5 which simplifies to Rung N-3

Then she was on rung N-3 + 6 which simplifies to Rung N+3

Then she was at Rung N+3 + 4 which simplifies to Rung N+7

So she was at rung 2N-1, since the ladder has 2N-1 rungs.

Therefore

N+7 = 2N-1

Solve that and get

8 = N

So the ladder had 2N-1 = 2(8)-1 = 16-1 = 15 rungs,

----------

Checking:


Kathy stood on the middle rung of a ladder. 

Rung 15
Rung 14
Rung 13
Rung 12
Rung 11
Rung 10
Rung 9
Rung 8  <-- She started on the middle rung 8.
Rung 7
Rung 6
Rung 5
Rung 4
Rung 3
Rung 2
Rung 1

She climbed up 2 rungs, 

Rung 14
Rung 13
Rung 12
Rung 11
Rung 10  <-- Then she was here. 8+2 = 10
Rung 9   
Rung 8
Rung 7   
Rung 6
Rung 5
Rung 4
Rung 3
Rung 2
Rung 1

moved down 5, 

Rung 15
Rung 14
Rung 13
Rung 12
Rung 11
Rung 10
Rung 9
Rung 8
Rung 7   
Rung 6
Rung 5  <-- Then she was here. 10-5 = 5
Rung 4
Rung 3
Rung 2
Rung 1

then climbed up 6 rugs, 

Rung 15
Rung 14
Rung 13
Rung 12
Rung 11  <-- then she was here. 5+6 = 11 
Rung 10
Rung 9
Rung 8
Rung 7   
Rung 6
Rung 5
Rung 4
Rung 3
Rung 2
Rung 1

and up 4 more to get to the top of the ladder.

Rung 15  <-- then she was here at the top of the ladder. 11+4=15.  So it checks.
Rung 14
Rung 13
Rung 12
Rung 11
Rung 10
Rung 9
Rung 8
Rung 7   
Rung 6
Rung 5
Rung 4
Rung 3
Rung 2
Rung 1  

Answer: 15 rungs.

Edwin

Let number of rungs be R

Then middle, or median rung = 

Moving up and down the ladder, we get:  



R + 1 + 14 = 2R -------- Multiplying by LCD, 2

R + 15 = 2R

R – 2R = - 15

- R = - 15

R, or number of rungs = , or  

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