September 2018
Problem of the Month

Mr. P's Phone Number

Mr. P's phone number (Area code / Exchange / Number) consists of ten digits with no duplicates.

The three digits in the area code are in descending order, and the the four digits in the number are in ascending order.

The sum of the three numbers in the exchange is 18.

The three digits of the exchange are not in ascending or descending order.

The third digit in the exchange is one less than the last digit in the number.

The telephone number is divisible by five.

What is Mr. P's phone number?

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Disclaimer: Only the first five digits (area code plus the first two digits of the exchange) are really Mr. P's phone number.   The last five digits had to be changed to make up this problem!

Solution to the Problem:

Mr. P's phone number is:
970 / 684 / 1235.

Since the number is divisible by 5, the last digit of the number must be 0 or 5.

Since the third digit of the exchange must be one less than the last digit of the number, the last digit of the number must be 5 and the third digit of the exchange must be 4.

Since the sum of the digits in the exchange is 18, the first two digits must add up to 14.   The only possibilities are 9 and 5, 8 and 6, and 7 and 7.   The two digits cannot be 7 and 7 (no duplicates) and cannot be 9 and 5 (5 is already the last digit of the number).   Since the numbers in the exchange are not in ascending or descending order, the exchange must be 684.

Since the digits in the number are in ascending order, the number must be 1235, leaving 970 as the area code.

James Alarie sent in the following solution:
      9 7 0 - 6 8 4 - 1 2 3 5
      9 7 1 - 6 8 4 - 0 2 3 5
      9 7 2 - 6 8 4 - 0 1 3 5
      9 7 3 - 6 8 4 - 0 1 2 5

      Does your wife know about your
      "other" three phone numbers?

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I did not think about zero as the first digit of the number, so James is exactly right -- there are four solutions to this problem!

To make this a better problem, I should have added the following clue:
The third digit in my area code is one less than the first digit in my phone number.

Rob Miles also sent in the four solutions to the problem, but eliminated three of them because they were not legitimate area codes.   Only 970 is an actual area code.

Correctly solved by:

1. James Alarie  **	Flint, Michigan
2. Bryce Villanueva	University of Central Florida, Orlando, Florida
3. Elizabeth Lawrence	Delta High School, Delta, Colorado
4. Maura Flake	Mountain View High School, Mountain View, Wyoming
5. Kelly Stubblefield	Mobile, Alabama
6. Rob Miles   **	Northbrook, Illinois
7. Nicolle Leonrad	Mountain View High School, Mountain View, Wyoming
8. Michael Stoll	Mountain View High School, Mountain View, Wyoming
9. Caleb Frazier	Delta High School, Delta, Colorado
10. Boomessh Kumar **	Bangalore, Karnataka, India
11. Dmitriy Chernoshey **	Darien, Illinois
12. Carlota Pombar Rodriguez	Mountain View High School, Mountain View, Wyoming
13. Brijesh Dave	Mumbai City, Maharashtra, India
14. Ivy Joseph	Pune, Maharashtra, India
15. Hunter Gross	Mountain View High School, Mountain View, Wyoming
16. Kaylee Gross	Mountain View High School, Mountain View, Wyoming
17. Briggin Bluemel	Mountain View High School, Mountain View, Wyoming
18. Makayla Kortz	Delta High School, Delta, Colorado

** Extra credit for finding all four solutions!

Send any comments or questions to: David Pleacher