How Cheenta works to ensure student success?

Explore the Back-StoryContent

[hide]

Try this beautiful Problem based on Counting Principle from 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 Reading

Source of the Problem

Answer

AMC 2020 PROBLEM 21

28

Hint 1

Hint 2

Hint 3

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,

Content

[hide]

Try this beautiful Problem based on Counting Principle from 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 Reading

Source of the Problem

Answer

AMC 2020 PROBLEM 21

28

Hint 1

Hint 2

Hint 3

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,

Cheenta is a knowledge partner of Aditya Birla Education Academy

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.

JOIN TRIALAcademic Programs

Free Resources

Why Cheenta?

Google