Palindrome Percentage

Number Theory Level 2

What is the percentage of palindrome numbers between 1 and 10000, both included?

1.96 1.92 1.98 1.9 1.94 2

Arnau PadresMasdemont by Arnau PadresMasdemont , 19, Spain

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1 solution

  • From 1 to 9, there are 9 (all of them).
  • From 10 to 99, there are 9 (only multiples of 11: 11, 22, 33...).
  • From 100 to 999, there are 90 (both 1st and 3rd position have 9 possible numbers: 1 to 9; and the 2nd position has 10: 0 to 9. 9x10=90).
  • From 1000 to 9999 there are 90 (1st and 4th, 9 possibilities; 2nd and 3rd, 10 possibilities).
  • 10000 is not palindrome.

9 + 9 + 90 + 90 10000 \frac{9+9+90+90}{10000} x 100 = 1.98

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