Problem 28 · 2011 Math Kangaroo
Stretch
Number Theory
cryptarithmfactorization
Which is the smallest possible positive whole-number value of the expression K × A × N × G × A × R × O × OG × A × M × E if different letters stand for different digits not equal to 0, and the same letters stand for the same digits?
Show answer
Answer: B — 2
Show hints
Hint 1 of 2
First simplify by cancelling the letters that appear in both top and bottom.
Still stuck? Show hint 2 →
Hint 2 of 2
Then assign distinct digits so the remaining fraction is a small whole number.
Show solution
Approach: cancel repeated letters, then make the leftover product smallest
- The expression is K·A·N·G·A·R·O·O divided by G·A·M·E; the G and one A cancel.
- What is left is K·A·N·R·O·O / (M·E) with distinct nonzero digits.
- Choosing digits so the bottom nearly matches the top makes the smallest whole-number value 2.
Mark:
· log in to save