Problem 16 · 2018 Math Kangaroo
Hard
Logic & Word Problems
Before the football game Real Madrid vs. Manchester United, five predictions were made:
(i) The game will not end in a draw. (ii) Real Madrid will score at least one goal. (iii) Real Madrid will not lose. (iv) Real Madrid will win. (v) Exactly three goals will be scored in total.
It turns out that exactly three of these predictions come true. How many goals did Real Madrid score?
Show answer
Answer: B — 1
Show hints
Hint 1 of 2
Notice that 'Real Madrid will win' would make several other predictions true at once.
Still stuck? Show hint 2 →
Hint 2 of 2
Since exactly three are true, decide which statements must be false.
Show solution
Approach: logical elimination with the 'exactly three true' constraint
- If 'Real Madrid wins' were true, then 'not a draw', 'scores at least 1', and 'does not lose' would all be true too — four true. So 'wins' is false.
- A draw makes too few statements true, so Real Madrid loses.
- Then 'not a draw', 'scores at least one goal', and 'exactly 3 goals total' are the three true ones, with 'wins' and 'does not lose' false.
- A loss such as 1–2 (total 3) fits — Real Madrid scored 1 goal.
Mark:
· log in to save