Solution
There are two solutions to this puzzle: 12,10 and 14,12.
The second one missed my sight while checking for uniqueness. I apologise for your time.
Solving hints:
- Since the son says "It's not enough information", there must be more than one right-triangle having the perimeter equal to his age.
So the perimeter can not be 7 for example, because it would only yield the 1-3-3,16 triangle.
- Since the son says "It's not enough either", there must be more than one right-triangle having the area equal to his father's age, which also have the same perimeter.
So the perimeter can not be 21 for example, because it would yield:
1-10-10,05 and
3-9-9,48
triangles, but they have different areas. Therefore the son could have easily found the one with the area equal to his father's age.
- Old mathematician says "Your father was younger than you are when you were born". Therefore the son's age must be more than half of his father's if he was alive.
- There are three possible perimeters satisfying these criterias: 30 (with area 40), 37 (with area 60) and 44 (with area 84).
But it can't be 30, because the father would have been 10 years old when the son was born, which is biologically not possible.
|
|
|
 |
12, 10 (or 14, 12)
54 correct, 26 incorrect answers.
Rated 4.02 by 105 competitors who attended PQRST 06.
01
02
03
04
05
06
07
08
09
10
|
|
|
