Counting Palindromes

Number Theory Level 2

How many different 7 digit palindromes are there?

Uncountable 10000 1000 9000 5000

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

Mahdi Raza
May 29, 2020
  • 9 options for 1st and 7th position
  • 10 options for 2nd and 6th position
  • 10 options for 3rd and 5th position
  • 10 options of 4th position

9 × 10 × 10 × 10 = 9000 9 \times 10 \times 10 \times 10 = 9000

2 Helpful 1 Interesting 1 Brilliant 0 Confused

In a seven digit palindrome, we have 4 sets of identical digits. The 1st and 7th, the 2nd and 6th, the 3rd and 5th, and the 4th. Looking for the amount of possibilities for each digit, we find the 1st and 7th can only have 9 choices (because the 1st can't 0), and the others 3 sets have 10 choices. Solving the amount palindromes, we have 9×10×10×10=9000

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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