A problem from the Stanford University Competitive Examination in Mathematics:
How old is the captain, how many children has he, and how long is his boat? Given the product 32118 of the three desired numbers (integers). The length of the boat is given in feet (is several feet), the captain has both sons and daughters, he has more years than children, but he is not yet one hundred years old.
|
SelectClick for Answer |
The prime factors of 32,118 are 2, 3, 53, and 101. There are only six ways to decompose it into three factors that are different from 1:
6 × 53 × 101
3 × 101 × 106
3 × 53 × 202
2 × 101 × 159
2 × 53 × 303
2 × 3 × 5,353
Of these possibilities, only the first includes two factors in the range from 4 (the minimum number of children) to 99 (the captain’s maximum age). So the captain has 6 children, he’s 53 years old, and his boat is 101 feet long.
From George Polya, The Stanford Mathematics Problem Book, 1974.
|
