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?

a  for after: 2182

b for before: 1846

d2:  for difficulty

s :  for solution

S=24m+22=24*(7*n+6)=168n+166      eq 1

c for checking:   inserting (10,11,12) into  eq 1 yields
(1846,2014,2182).

Posted by Ady TZIDON on 2014-12-11 07:58:00