June 2017
Problem of the Month

The Omnipotent Key
by Miko Zhang, Delta High School, Delta, Colorado

Find an omnipotent key (a number) that can open four locks using the following clues:

(1) The first lock is an even number.

(2) The second lock is a number whose factors add up to 42.

(3) The third lock is a multiple of 2 and 5.

(4) The fourth lock is a double digit.

What is the number on the omnipotent key?

Solution to the Problem:

The number on the omnipotent key is 20.

Lock #1: The number could be 0, 2, 4, 6,
                8, 10, 12, ...

Lock #2: The number must be either
                20, 26, or 41 since
    20 + 10 + 5 + 4 + 2 + 1 = 42 and
    26 + 13 + 2 + 1 = 42 and
    41 + 1 = 42

Lock #3: The number must be a multiple
                of 10: 10, 20, 30, 40, 50, 60, ...

Lock #4: The number must be 10, 11,
                12, 13, ... 99.

Correctly solved by:

1. Anna Vice and Eliza Sheffield	Tuscaloosa, Alabama
2. Brijesh Dave	Mumbai City, Maharashtra, India
3. SreeRoopa Sankararaman	Singapore, Singapore

Send any comments or questions to: David Pleacher