4

“This might interest you, master Yoda and master Obi-Wan,” said Anakin. “My age and the ages of each my three children are prime numbers, and the sum of our ages is 50.” “In that case,” said master Obi-Wan, who knew Anakin’s age, “I can tell you the ages of your three children.” “Oh, if like this,” said master Yoda, who didn’t know the age of Anakin, “I can tell you, after n years, the total of your three children ages will become twice as your age.” “How you know that, master Yoda?” said Anakin after he did the calculation. “Through the Force, I see.” said master Yoda.

Based on the above dialogue, what is the value of n?
sree
  • 41

2 Answers2

2

Let A be Anakin's age and $c_1, c_2, c_3$ be the ages of his three children. These three numbers must be prime. $A\in \{ 47, 43, 41, 37, 31, 29, 23 ... \}$. We can eliminate 47 because 50-47=3=$c_1+c_2+c_3$ does not hold for any prime c's. Additionally, we cannot have A=41 because then 50-41=9=5+2+2=3+3+3, so we cannot uniquely determine the age of his children. Continuing in this way we can see that we must have A=43 and that $c_1=3, c_2=2, c_3=2$.

The condition regarding n is the following:

$(c_1 + n) + (c_2 + n) + (c_3 + n) = 7+3n = 2(A+n) = 2(43+n)$.

Solving for n gives us $n=79$.

Nitin Passa
  • 326
0

$\large n = 73 $ $$ \begin{array}{rr} \mbox{Before}& \\[1cm] \mbox{child}\ 1 & 3 \\ \mbox{child}\ 2 & 3 \\ \mbox{child}\ 3 & 3 \\ \mbox{Father} & 41 \end{array} \qquad\qquad\left\{% \begin{array}{rr} &\mbox{After}\ n = 73\ \mbox{years} \\[1cm] \mbox{child}\ 1 & 76 \\ \mbox{child}\ 2 & 76 \\ \mbox{child}\ 3 & 76 \\ \mbox{Father} & 114 \end{array}\right. $$

$$ 228 = 76 + 76 +76 = 2 \times 114 = 228 $$

Felix Marin
  • 89,464