[Interesting question] cake issue

For a birthday banquet, the total number of participants may be five or nine. If the birthday cake needs to be cut in advance and the split size can be different, ask the minimum cut in size, can the cake be evenly distributed to each participant, no matter the total number is 5 or 9?

13 blocks:

1/9 RMB 5

1/45 4

4/45 4

 

PS: I don't know how to prove it, and I'm not sure if 13 is the correct answer. If you have a strict proof process or any good proof methods, please leave a message, thank you!

[Interesting question] cake issue