The year 2014 when divided by 24 yields a quotient of 83 and a remainder of 22. The number 83 when divided by 7 yields a quotient of 11 and a remainder of 6. So, the number 2014 when successively divided by 24 and 7 yields the respective remainders of 22 and 6.

Which year comes next that yields the respective remainders of 22 and 6 upon successive divisions by 24 and 7? Which year before 2014 has this property?

It is enough, knowing 7 and 24 are relatively prime, to say this happens every 7*24=168 years.

2014-168=1846
2014+168=2182

It doesn't really matter what the remainders are.

Posted by Jer on 2014-12-11 13:36:40