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.

Find the number which has 8 divisors, such that the product of the
divisors is 331776.

Eminit

Age 11 to 14 Challenge Level:

The number 8888...88M9999...99 is divisible by 7 and it starts
with the digit 8 repeated 50 times and ends with the digit 9
repeated 50 times. What is the value of the digit M?