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# chess board riddle

6 replies to this topic

### #1 jake_harper

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Posted 30 January 2013 - 06:16 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

• 0

### #2 bushindo

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Posted 30 January 2013 - 06:25 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

• 0

### #3 jake_harper

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Posted 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.

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### #4 phil1882

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Posted 30 January 2013 - 07:54 AM

Edited by phil1882, 30 January 2013 - 07:56 AM.

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### #5 Prime

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Posted 30 January 2013 - 08:39 AM

Hello Jake. Welcome to the Den.

Bushindo's answer has the right logic. His numbers are slightly off. I'll put my solution inside Spoiler, to let other people tackle this problem on their own.

Spoiler for solution

Edited by Prime, 30 January 2013 - 08:40 AM.

• 0

Past prime, actually.

### #6 jake_harper

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Posted 30 January 2013 - 08:49 AM

Thank you all

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### #7 bonanova

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Posted 30 January 2013 - 08:51 AM

Another difference in people's answers might stem from the "no backtracking" stricture in the OP.

Bushindo interpreted that to mean only up and only right [no down and no left] moves may be made.

A less restrictive interpretation would give a higher answer.

One such might permit revisiting a previously occupied square but not to retracing any piece of your path.

That is, not reversing any previous move between squares.

No backtracking, therefore, should be clarified.

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Vidi vici veni.

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