Question 1016489
 A certain number leaves a remainder of 4 when divided by 5,
The number has to end in a 4 or a 9
:
 a remainder of 5 when divided by 6, and
multiples of 6 +5 ending in 4 or 9
29, 59, 89, 119, 149, 179, 209, 239, 269
:
 a remainder of 6 when divided by 7.
multiples of 7 + 6 ending  in 9 (4 does not appear in the previous list)
69, 139, 209, 279
:
 Find the smallest number that satisfies these conditions.
looks like 209 is the winner!