Latin Numbers

Can you create a Latin Square from multiples of a six digit number?

Repeaters

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Six Times Five

Stage: 3 Challenge Level:

How many six-digit numbers are there which DO NOT contain a $5$?