
Martin Gardner is a very famous problem proposer. He wrote
the Mathematical Games column in Scientific American for twentyfive years. Here
are two problems from his book My Best Mathematical and Logic Puzzles.
1. Write down any threedigit number, and then repeat the digits in the same
order to make a sixdigit number (e.g., 394,394). Divide this sixdigit number
by 7 (there won’t be a remainder), divide the result by 11 (again, there won’t
be a remainder), and divide this last result by 13 (there still won’t be a
remainder!). Show that the number you now have is equal to the threedigit
number that you started with!
2. Only two digits in the following long division problem are revealed. Find the other digits.