Problem 19 · 2014 Math Kangaroo
Stretch
Logic & Word Problems
careful-counting
Elisabeth sorts the cards shown above. With each move she is allowed to swap any two cards with each other. What is the smallest number of moves she needs in order to get the word KANGAROO?
Show answer
Answer: B — 3
Show hints
Hint 1 of 3
Write KANGAROO under the cards and mark every letter that is already in the right place.
Still stuck? Show hint 2 →
Hint 2 of 3
Only the wrong letters need to move, so look at just those.
Still stuck? Show hint 3 →
Hint 3 of 3
One swap trades two cards, so it can drop two wrong letters into the right spots at once.
Show solution
Approach: count the swaps that fix two misplaced letters at a time
- O A R G O N K A must become K A N G A R O O; the A and the G are already in place.
- The six remaining letters split into three pairs that each swap into place: (K↔O), (N↔R), (A↔O).
- Three swaps fix all six, and fewer is impossible.
- Answer: 3.
Mark:
· log in to save