Answer to September 13, 1999 Problem

Judge Handley's Phone Number
adapted from a problem
in issue 91 of Recreational & Educational Computing

Judge John Handley had a ten digit telephone number (including area code) in which each digit, 0 through 9, appears once.
The first digit on the left is divisible by 1,
the first two digits form a number divisible by 2,
the first three digits form a number divisible by 3,
the first four digits form a number divisible by 4,
and so on, until we get to the whole 10-digit number which is divisible by 10.

What is Judge Handley's phone number?

Answer to the Problem:

The Judge's Phone number was (381) 654-7290.

To solve the problem, begin with the 10th digit. It must be 0 because the whole number is divisible by 10.
The fifth digit must be a 5 because the first five digits must be divisible by 5 (divisibility by 5 requires the last digit to be a 0 or a 5, but the 0 is taken).
The numbers 2, 4, 6, and 8 must be the 2nd, 4th, 6th, and 8th digits because of the divisibility rules.
There are 24 different ways that those digits may be arranged.
Hence, the numbers 1, 3, 7, and 9 must be the 1st, 3rd, 7th, and 9th digits, and there are 24 ways in which they can be arranged.

Some logic and a knowledge of the divisibility rules yield the required solution 381-654-7290.


Correctly solved by:

1. Tom Marino Winchester, VA
2. Richard Mocarski Winchester, VA
3. Jon Pence Winchester, VA