Combinatorics...
Someone talks to a guy, and asks, Give me the age of my three sons, The other guy asks for some clues: The product of the age of the three sons (of someone) is equal to 36. "I can't figure out their ages." says solver
The sum of the ages of the three brothers is the same as the number of windows you can see in this building (points to some building). "I still can't figure out their ages." says solver The oldest has blue eyes. "Now I know their ages." says solver!.
Can you figure out their age?
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1 solution
Solution:
Only possibilities :
(age 1, age 2, age 3 ; sum of the ages)
(1, 1, 36 ; 38)
(1, 2, 18 ; 21)
(1, 3, 12 ; 16)
(1, 4, 9 ; 14)
(1, 6, 6 ; 13) * * *
(2, 2, 9 ; 13) * * *
(2, 3, 6 ; 11)
(3, 3, 4 ; 10)
Every combination of possible ages with a product of 36 contain its own unique sum of ages : except for 1, 6, 6 & 2, 2, 9, both of which share the sum of 13. Since the solver can't figure out the ages after looking at the windows, the nb of windows must be 13. Now, the next clue is that the 'oldest' son has blue eyes which implies that there is one oldest son. We, therefore, figure out the 1, 6, 6 and the ages of the son must be 2, 2 & 9 years old