Two Social Security numbers (see Exercise 8.12) match zeros if a digit of one number is zero iff the corresponding digit of the other is also zero. In other words, the zeros in the two numbers appear...

Two Social Security numbers (see Exercise 8.12) match zeros if a digit of one number is zero iff the corresponding digit of the other is also zero. In other words, the zeros in the two numbers appear in exactly the same positions. For example, the Social Security numbers 120-90-1109 and 430-20-5402 have matching zeros. Prove: Given a collection of 513 Social Security numbers, there must be two that match zeros.