🚀 go-pugleaf

Feng Liu (liuf@bnr.ca) wrote:

: A person would like to go from a to b in the following diagram,
: one step at a time. No retrieving back or standing still is 
: allowed so that the total no. of steps is always (X+Y) Steps. There
: are many alternative routes between a and b by changing the
: sequence of X direction steps and Y direction. For example, the
: route can be a->c->b or a->d->b or a->e->f->g->h->i->j->b.
: What is the total number of routes all together? 

<<Hint deleted for brevity>>

:       c|<--- X Steps ----->| b
: 	+----+----+----+----+ -
: 	|    |    |    |    | ^
: 	|    |    |h   |i  j| |
: 	+----+----+----+----+ 
: 	|    |    |    |    | Y Steps
: 	|    |f   |g   |    |
: 	+----+----+----+----+
: 	|    |    |    |    | |
: 	|    |    |    |    | V
: 	+----+----+----+----+ -
: 	a    e                d

Two hints and a comment:

Hint 1)  Compare the numbers from different grids with the numbers in 
Pascal's triangle.

Hint 2)  Look for a key marked "nCr" on your calculator.  (Not all 
calculators have it.)  This is the "Choice function" or "Combination 
function" from combinatorics.

Comment)  I am watching a variation of this right now!  The "Plinko" game 
on the game show "The Price is Right"!
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