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# jake_harper

Member Since 30 Jan 2013
Offline Last Active Jan 30 2013 10:08 AM

### In Topic: chess board riddle

30 January 2013 - 08:49 AM

Thank you all

### In Topic: chess board riddle

30 January 2013 - 06:42 AM

I came across this somewhere on the web.

A pawn is sitting at one corner of an 8X8 chess board. It can take one step at a time in the horizontal or vertical direction (not diagonal). What is total number of ways in which it can reach the diagonally opposite end given that the pawn always tries to go towards the destination (i.e. no back-tracking).

I came up with an answer. Wanted to see whether it is the correct approach. Thank you

Hope you will enjoy

My guess

Spoiler for

Can you explain why you limit the number of squares that can form a path to 16? Shouldn't it be 64-2=62.

The approach I took was a bit different.

assume the pawn starts from the bottom right square. According to the given condition he can move to any square on the board while reaching the target. The pawn has two options at each square except for the squares lying on the leftmost column and topmost row (see the attached image)

based on this: 2*(64-2-14)*14 is my answer.