Problem 7 · 2019 Math Kangaroo
Medium
Number Theory
digit-sumplace-value
Reading from the left, what is the first digit of the smallest positive integer whose digit sum is 2019?
Show answer
Answer: B — 3
Show hints
Hint 1 of 2
To make a number small, use as few digits as possible — so pack digit value with 9s.
Still stuck? Show hint 2 →
Hint 2 of 2
2019 = 224·9 + 3, so use 224 nines preceded by a leading digit equal to the leftover 3.
Show solution
Approach: build the smallest number with digit sum 2019 using mostly 9s
- To minimise the number of digits, use 9s: 2019 ÷ 9 = 224 remainder 3.
- So 224 nines give digit sum 2016; we still need 3 more.
- Put the extra 3 as the leading digit: the number is 3 followed by 224 nines.
- The first digit is 3 — answer (B).
Mark:
· log in to save