Playing with Digits

Digit Sums

A digit sum is found by adding all the digits of a number together.

Example: For the number $176$: $1 + 7 + 6 = 14$

For the number $68$: $6 + 8 = 14$

Interestingly, different numbers can have the same digit sum.

Properties

• Smallest Number with Digit Sum 14: To make the number small, we want fewer digits. To use fewer digits, we use the largest possible digits (9).
  • $14 - 9 = 5$. So digits are 5 and 9.
  • Smallest order: $59$.
• Largest 5-digit number with Digit Sum 14: We want the largest digits at the start.
  • $9, \dots$ (Remaining sum 5)
  • $95000$ (Sum: $9+5+0+0+0 = 14$).

Consecutive Digits Pattern

Calculate digit sums for consecutive digits:

1. $123 \rightarrow 1+2+3 = 6$
2. $234 \rightarrow 2+3+4 = 9$
3. $345 \rightarrow 3+4+5 = 12$

Observation: The sums increase by 3 each time. This is because each digit in the sequence increases by 1 ($1 \to 2$, $2 \to 3$, $3 \to 4$), so the total sum increases by $1+1+1 = 3$.