- #1
K Sengupta
- 113
- 0
Determine the value of “PRINCE” and “FIVE”, given that “PRINCE” is a perfect cube and “FIVE” is a perfect square. Each of the letters denote a different decimal digit and none of P and F can be zero.
The "A Prince and Five Puzzle" is a classic mathematical riddle that involves a prince, five daughters, and a jester. It is also known as the "Ages of the Daughters Puzzle" or the "Ages of the Princesses Puzzle".
The puzzle begins with a prince who wants to marry one of the king's five daughters. However, the king has set a challenge for the prince - he must correctly guess the ages of all five daughters in order to marry one of them.
The rules of the puzzle are as follows:
- The ages of the daughters must be whole numbers.
- The sum of the ages of the five daughters is equal to the prince's age.
- The product of the ages of the five daughters is equal to the year of the puzzle.
- Each daughter's age is unique and none of them are the same as the prince's age.
The solution to the puzzle is that the prince's age is 36, and the ages of the five daughters are 1, 6, 8, 9, and 12. This satisfies all of the rules of the puzzle and allows the prince to marry one of the daughters.
The "A Prince and Five Puzzle" is a popular example of a diophantine equation, which is an equation where the variables are restricted to integers. It also demonstrates the use of logic and problem-solving skills in mathematics.