Question 159
Ben considers year $N$ lucky for a person if $N$ is divisible by his/her age (as a whole number of years) on 1st January of that year, e.g. $2016$ is lucky for someone whose age is $2$ or $3$ or $4$, but not for someone whose age is $5$. Ben was surprised to discover that both $2015$ and $2016$ were lucky for himself and they were also lucky for his daughter Amy (who was born prior to $2015$). Even though Ben's last lucky year before $2015$ was more than a decade earlier, he remembers that it had also been a lucky year for his father, Chris!
What is the least age difference between Amy and Chris, given that Chris is not yet $100$ years old? Your answer should be in years and days e.g. "30 years and 364 days". You may assume that parents are always at least fifteen years older than their children. (Note that $2015 = 5 \cdot 13 \cdot 31$ and $2016 = 2^5 \cdot 3^2 \cdot 7$.)
What is the least age difference between Amy and Chris, given that Chris is not yet $100$ years old? Your answer should be in years and days e.g. "30 years and 364 days". You may assume that parents are always at least fifteen years older than their children. (Note that $2015 = 5 \cdot 13 \cdot 31$ and $2016 = 2^5 \cdot 3^2 \cdot 7$.)