# How many digits are written?: visual puzzle | SwaVid

Write every whole number from 1 through 100 with no spaces. How many digits do you write in total? See the complete step-by-step solution.

Canonical: https://www.swavid.com/puzzles/counting-digits

Source: https://www.swavid.com/puzzles/counting-digits

# How many digits are written?

## 192 digits.

### One-digit numbers

### Two-digit numbers

### Three-digit numbers

SwaVid visual puzzle

Write every whole number from 1 through 100 with no spaces. How many digits do you write in total?

Detailed solution

Group the numbers by how many digits they have.

1 to 9 use one digit each.

10 to 99 is 90 numbers with two digits each.

Only 100 has three digits. Add everything up.

Answering 100 counts numbers, not digits. Answering 200 forgets that 1 to 9 are single digits.

- 1 One-digit numbers 1 to 9 use one digit each. 9 × 1 = 9
- 2 Two-digit numbers 10 to 99 is 90 numbers with two digits each. 90 × 2 = 180
- 3 Three-digit numbers Only 100 has three digits. Add everything up. 9 + 180 + 3 = 192

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