Prince Zrychlený invited Princess Zpomalená to his castle. When she took too long, he set out to meet her. After two days of travel, he met her at one fifth of her journey. Together, they continued their journey twice as fast as when the princess was traveling alone. They arrived at Prince's castle the second Saturday after their meeting. Which day did they meet, if the princess set out from her castle on Friday?

(M. Dillingerová)
Let's outline the distance between the castles of Princess Slowed and Prince Accelerated. If

![](https://cdn.mathpix.com/cropped/2024_04_17_3b8c55268a64867bcc1ag-1.jpg?height=171&width=1011&top_left_y=897&top_left_x=548)

the princess walked the first fifth of the journey in $d$ days, then she had to cover the remaining distance in $\frac{1}{2} 4 d = 2 d$ days. We know that $7 < 2 d < 15$. We try different integer values of $d$. The only one that correctly results in the princess setting out on a Friday is $d = 5$. The prince and princess met on Wednesday.