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# AMC 8 2020 Problem 21 | Counting Principle

Try this beautiful Problem based on Counting Principle from AMC 8, 2020 Problem 21.

## Counting Principle Problem: AMC 8 2020 Problem 21

A game board consists of 64 squares that alternate in color between black and white. The figure below shows square $P$ in the bottom row and square $Q$ in the top row. A marker is placed at $P$. A step consists of moving the marker onto one of the adjoining white squares in the row above. How many 7 -step paths are there from $P$ to $Q$ ? (The figure shows a sample path.)

• 28
• 30
• 32
• 33
• 35

Game problem

Chess board

combination

## Suggested Book | Source | Answer

AMC 2020 PROBLEM 21

28

## Try with Hints

See that

the number of ways to move from  P to that square is the sum of the numbers of ways to move from P to each of the white squares immediately beneath it

Try to construct a diagram and write the number of ways we can step onto that square from P which is calculated as the sum of the numbers on the white squares immediately beneath that square (and thus will represent the number of ways to remove from P to that square, as already stated).

So the diagram will look like,

AMC-AIME Problem at Cheenta

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Try this beautiful Problem based on Counting Principle from AMC 8, 2020 Problem 21.

## Counting Principle Problem: AMC 8 2020 Problem 21

A game board consists of 64 squares that alternate in color between black and white. The figure below shows square $P$ in the bottom row and square $Q$ in the top row. A marker is placed at $P$. A step consists of moving the marker onto one of the adjoining white squares in the row above. How many 7 -step paths are there from $P$ to $Q$ ? (The figure shows a sample path.)

• 28
• 30
• 32
• 33
• 35

Game problem

Chess board

combination

## Suggested Book | Source | Answer

AMC 2020 PROBLEM 21

28

## Try with Hints

See that

the number of ways to move from  P to that square is the sum of the numbers of ways to move from P to each of the white squares immediately beneath it

Try to construct a diagram and write the number of ways we can step onto that square from P which is calculated as the sum of the numbers on the white squares immediately beneath that square (and thus will represent the number of ways to remove from P to that square, as already stated).

So the diagram will look like,

AMC-AIME Problem at Cheenta

## Subscribe to Cheenta at Youtube

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