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From 1-100, it appears 20 times, in 19 different numbers.

  • 5
  • 15
  • 25
  • 35
  • 45
  • 50
  • 51
  • 52
  • 53
  • 54
  • 55
  • 56
  • 57
  • 58
  • 59
  • 65
  • 75
  • 85
  • 95

For every interval of one hundred after that (101-200, 201-300, etc.) except for 500, it will be the same amount of fives. So, 20 instances times 9 different intervals (still excluding 500-599), there are 180 fives.

Now we'll consider 500-599. From 0-99, there are 100 numbers, so there are also 100 numbers from 500-599. That means there is an extra 100 fives, for each 5 in the hundreds place. Add that to the original 20 from the tens and ones place, and there are 120 fives between 500-599.

When we add that 120 on the our other 180, we arrive at the grand total of 300 fives between 1-1000.

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Q: How many times does the number 5 appear from the numbers 1-1000?
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