## Thursday, 8 December 2011

### Puzzle-28 (CAT-2004)

In the below figure, the lines represent one way roads allowing travel only northwards or only westwards. Along how many distinct routes can a car reach point B from point A?
 B ↑ North ßWest A

(1)15               (2)56               (3)120             (4)336
Solution follows here:
Solution:
The number of Horizontal lines required to reach B = 5
The number of Vertical lines required to reach B     = 3
H         H         H         H         H         V          V          V
Observe that whatever the path taken to reach B starting from A, the number of horizontal lines required is 5 and vertical lines required is 3. The beauty here is mathematically we need to find different combinations of these 5+3 = 8 lines
This is nothing but the number of ways of arranging (p+q) things where p things are of similar type and q things are of similar type. Formula here is (p+q)! / (p!q!)
Number of ways = (5+3)!/(5!3!) = 8!/(5!3!) = 8*7*6/3*2 = 56

1. Comment on puzzle-3 can be verified for the logic:

2. Dear Sankar

Nice to see u r Blog. A Great Attempt. Hearty Congratulations All The Best

There will be lot of changes to take place in the near future in school education in the distant mode

Warn Regards

Raghu
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