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Algebra Arithmetic Combinatorics Math Olympiad PRMO

Two Arrangements | PRMO 2019 | Question 5

Try this beautiful problem from the Pre-RMO, 2019 based on Two Arrangements. You may use sequential hints to solve the problem.

Try this beautiful problem from the PRMO, 2019 based on Two arrangements.

Two arrangements – PRMO 2019


Five persons wearing badges with numbers 1,2,3,4,5 are seated on 5 chairs around a circular table. Find the number of ways they be seated that no two persons whose badges have consecutive numbers are seated next to each other.

  • is 107
  • is 10
  • is 840
  • cannot be determined from the given information

Key Concepts


Arrangement

Algebra

Number Theory

Check the Answer


But try the problem first…

Answer: is 10.

Source
Suggested Reading

PRMO, 2019, Question 5

Combinatorics by Brualdi

Try with Hints


First hint

Here they may seat in circular way such that 1,3,5,2,4 and again 1

Second Hint

then they may seat in another circular way 1,4,2,5,3 and again 1

Final Step

Then number of ways = (2)(5) =10.

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