Warning: Causes Visions
Robin B. correctly identified the age at which Bob Frank saw himself live in his turkey induced vision and nets a $50 gift certificate from ThinkGeek!
Puzzle
The Frank family just finished up their Thanksgiving dinner. Bob Frank, the youngest cousin, capped off his dinner with half of a pumpkin pie. This was after four servings of Turkey, a ton of ham, sweet potatoes, corn, three rolls and stuffing. He’s already got the meat sweats, and now with the addition of all the sugar from the pie - Bob has gone into a walking food coma. Suddenly he becomes quite confused as to where he is and who all the people around him are. Bob looks around and the world is spinning. Suddenly he sees his whole life and death flash before his eyes - even the age at which he will die. He sees his youth lasted 1/6 of his life. In the next 1/12 of his life he had his first beard. At the end of the following 1/7 of his life, he got married. Five years later his daughter was born. His daughter lives exactly 1/2 of Bob’s life. Bob dies 4 years after the death of his daughter. How long did Bob live in his vision?
Solution
Diophantus was a Greek mathematician from Alexandria, commonly referred to as the father of algebra. He lived around 3rd century A.D. The point of that? Well, his life was described by an admirer of his by this algebraic riddle, which is what the puzzle above was based on.
1/6x + 1/12x + 1/7x + 5 + 1/2x + 4 = x
x=84
Or, Robin’s solution:
Proof derivation:
Let X = Bob’s age
Let Y = Bob’s daughters age
X = 2Y
X = (1/6)X + (1/12)X + (1/7)X + 5 + Y + 4
Merge two equations together and then solve for Y:
2Y = (1/6)X + (1/12)X + (1/7)X + Y + 9
Y = (1/6)X + (1/12)X + (1/7)X + 9
Y = (11/28)X + 9
Plug original X = 2Y equation into resultant equation above:
Y = (11/28)(2)Y + 9
Y = (22/28)Y + 9
Y = 42
X = 2Y = (2)(42) = 84
Thanks for playing and stay tuned for another puzzle on Monday!
