Answer to Question #239794 in Complex Analysis for laki

Question

   On the first day of the month, 4 customers come to a restaurant. Afterwards, those 4 customers come to the same restaurant once in 2,4,6 and 8 days respectively.

a)     On which day of the month, will all the four customers come back to the restaurant together?

b)     Briefly explain the technique you used to solve (a).

Answer 1

a)

The four customers come back to the restaurant together  on the 25^th day of the month.

b)

First client: $1, 3, 5, 7, 9, 11, 13, 15,17,19,21,23,\colorbox{aqua}{$25$},27,29$

Second client: $1, 5, 9, 13, 17, 21, \colorbox{aqua}{$25$}, 29$

Third client: $1, 7, 13, 19, \colorbox{aqua}{$25$}$

Fourth client: $1, 9, 17, \colorbox{aqua}{$25$}$