OpenOlympiad
Concept 17 of 19Advanced
Video

Counting specific digits in a range

Question: "How many times does the digit 3 appear between 1 and 100?"

Strategy: count by POSITION.

  1. Units place: 3, 13, 23, 33, 43, 53, 63, 73, 83, 93 → 10 appearances.
  2. Tens place: 30, 31, 32, …, 39 → 10 appearances.
  3. (Hundreds place: zero, since our range stops at 100.)
  4. Total: 10 + 10 = 20.

Note: 33 contains TWO 3s, but we count each appearance separately.

Example
How many 7s from 1 to 200?
Units: 7, 17, 27, …, 197 → 20.
Tens: 70, 71, …, 79 AND 170, 171, …, 179 → 20.
Total = 40.
💡 Tip:Always split by digit POSITION. Never try to list all numbers.
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5 questions to check what you just read.

0 / 5
  1. Q1.How many 5s appear from 1 to 50?
  2. Q2.How many 1s appear from 1 to 20?
  3. Q3.How many 7s appear from 1 to 100?
  4. Q4.How many 9s appear from 1 to 100?
  5. Q5.How many 3s appear from 100 to 199?