Grades 9-10 Video Solutions 2013-Level 9&10 Video Solutions 2013 problem26

Level 9&10 Video Solutions 2013 problem26

Video Transcription

Video Summary

Horatio needs to form 11 fractions using each number from 1 to 22 once, aiming for the maximum number of fractions with integer values. Focusing on minimizing issues with prime numbers less than 22, he selects 22/11, a fraction that reduces to an integer due to 11 being the largest divisor of 22. Along with 13/1, these are among the manageable primes. Certain primes like 17 and 19 will not form fractions that simplify to integers. By carefully pairing numbers, Horatio can achieve at most 10 fractions with integer values, leaving two primes unused. The answer is 10.

Keywords

fractions

integer values

prime numbers

Horatio

number pairing