Solution to: Odd Oranges
Assume the number of oranges is A. Then A-1 is divisible by 3, 5, 7, and 9. So, A-1 is a multiple of 5×7×9 = 315 (note: 9 is also a multiple of 3, so 3 must not be included!). We are looking for a value of N for which holds that 315×N + 1 is divisible by 11. After some trying it turns out that the smallest N for which this holds is N = 3. This means that the greengrocer has at least 946 oranges.
Note that for N = 14, 25, 36, etc. (so each time 11 more) it also holds that 315×N + 1 is divisible by 11.