• A number is divisible by 3 if the sum of its digits is divisible by 3. For example: 224055; 2+2+4+5+5=18, which is divisible by 3.
• A number is divisible by 4 if the last two digits are 00 or are divisible by 4.
• To test if a number is divisible by 7, take the last digit, double it, and subtract it from the remaining digits. Repeat until you can tell if the number is divisible by 7. For example: 59983; 5998-6=5992; 599-4=595; 59-10=49, which is divisible by 7.

1. Find a test for divisibility by 111.
2. Extending this, find a test for divisbility by any number consisting solely of 1's.

Source: An original extension of UofCF's Problem of the Week ending 11/9/97.