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October 15, 2020

Chessboard Problem | PRMO-2018 | Problem No-26

Try this beautiful Chessboard Problem based on Chessboard from PRMO - 2018.

Chessboard Problem - PRMO 2018- Problem 26

What is the number of ways in which one can choose 60 units square from a $11 \times 11$ chessboard such that no two chosen square have a side in common?


  • \(56\)
  • \(58\)
  • \(60\)
  • \(62\)
  • \(64\)

Key Concepts

Game problem

Chess board


Suggested Book | Source | Answer

Suggested Reading

Pre College Mathematics

Source of the problem

Prmo-2018, Problem-26

Check the answer here, but try the problem first


Try with Hints

<br>First Hint

Total no. of squares $=121$
Out of these, 61 squares can be placed diagonally. From these any 60 can be selected in ${ }^{61} C_{60}$ ways $=61$

Now can you finish the problem?

Second Hint

From the remaining 60 squares 60 can be chosen in any one way

Total equal to ${ }^{61} \mathrm{C}{60}+{ }^{60} \mathrm{C}{60}=61+1=62$

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