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. back to the puzzle