🦘 Math Kangaroo Grade All Felix 1-2 Ecolier 3-4 Benjamin 5-6 Kadett 7-8 Junior 9-10 Student 11-12 ⇄ switch contest
2015 Math Kangaroo

Problem 12

Problem 12 · 2015 Math Kangaroo Medium
Logic & Word Problems work-backwardoff-by-one

10 runners start in a running race. At the finish, there are 3 more runners behind Thomas than there are in front of him. In which position did Thomas finish?

Show answer
Answer: C — 4
Show hints
Hint 1 of 2
Besides Thomas there are 9 other runners, split into a front group and a back group.
Still stuck? Show hint 2 →
Hint 2 of 2
The back group is 3 bigger than the front group; try sharing the 9 runners so the back has 3 more.
Show solution
Approach: share the other 9 runners into front and back groups
  1. Take Thomas out for a moment: the other 9 runners are split into the ones in front and the ones behind.
  2. The back group must be 3 bigger than the front group, so split 9 into 3 in front and 6 behind (6 is 3 more than 3).
  3. With 3 runners in front of him, Thomas is the next one, so he is in 4th place.
  4. The answer is 4.
Mark: · log in to save