A family of 3 - a father, mother and son - are practising on a dart board. It has 3 shapes - a triangle, a circle and a square - on it. Scoring is as follows:
- Intersection of all 3 shapes - 5 points
- Intersection of exactly 2 shapes - 4 points
- Exactly in one shape - 3 points
- Outside all shapes, but on the board - 2 points
- Outside the board - 0 points
After the game, the board looked like this: (Each star is an arrow)
All 3 of them scored the same number of points.
Each of them also made a statement:
- Father: If I was the first to score in the square, then I scored at least one 2.
- Mother: If I was the first to score in the triangle, then my husband and my son did not score the same number of 2s as each other.
- Son: If I scored first in the circle, then I did not score more 2s than my mother.
Exactly one of them told the truth. Who scored the 5?
Note: Remember that, for any
Statement X: If A is true, then B is true.
we can conclude that
Statement X is false if and only if A is true and B is false.