If I write down all the numbers from 1 to 10,000, how many twos will I write down?

Step 1 - Start with the numbers from 1 to 10. Here, only the number 2 contains the digit 2. Step 2 - Take a look at the numbers 1 to 100. The number 2 occurs in every tenth, but it also occurs in the range of 20-29. Therefore, $10 * 2 = 20$ twos occur. Step 3 - The numbers 1 to 1000 contain ten hundreds, so we have at least $10 * 20 = 200$ twos. However, the numbers in the range of 200-299 also contain 100 twos extra, so the numbers 1 to 1000 contain 300 twos. Step 4 - In a similar way, we find that the numbers 1 to 10000 contain 4000 twos.

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