August 2021
Problem of the Month

Mystery Numbers

    6 + 4 = 210
    9 + 2 = 711
    8 + 5 = 313
    5 + 2 = 37
    7 + 6 = 113
    9 + 8 = 117
    10 + 6 = 416
    15 + 3 = 1218
    ?? + ?? = 123

Solution to the Problem:

12 + 11 = 123

The sum of the two numbers gives the last one or two digits, and the difference of the two numbers gives the first one or two digits.

Let a = first number and b = second.

There are two possibilities:
a + b = 3 and a - b = 12 or
a + b = 23 and a - b = 1

Solving the first set of possibilities, you get 2a = 15 and a = 7.5 which does not work.

Solving the second set, you get 2a = 24, so a = 12 and b = 11 which does work.

However, Veena Mg suggested that negative numbers and fractions should be allowed since I did not specify positive numbers, so she added the solution of 7.5 and -4.5.

(x - y) = 12
(x + y) = 3
Adding both gives
2x = 15
x = 7.5
y = 3 - 7.5 = -4.5

7.5 - (-4.5) = 12
7.5 + (-4.5) = 3

Correctly solved by:

1. Veena Mg	Bangalore, Karnataka, India
2. Colin (Yowie) Bowey	Beechworth, Victoria, Australia
3. Hari Kishan	Meerut, Uttar Pradesh, India
4. Parnkaew Rujivanarom	----------
5. Emily Packard	Central High School, Grand Junction, Colorado
6. Sara Gagler	Central High School, Grand Junction, Colorado
7. Veronica Sanchez	Central High School, Grand Junction, Colorado
8. Jonathan Punke	Bremen High School, Midlothian, Illinois
9. Shifa Panjwani	Hyderabad, Telangana, India
10. Sambhavi Verma	New Delhi, Delhi, India
11. Mya Marquez	Central High School, Grand Junction, Colorado
12. Jordan Sollinger	Woodridge High School, Peninsula, Ohio
13. Ryan Huff	Central High School, Grand Junction, Colorado
14. Kelly Stubblefield	Mobile, Alabama
15. Ivy Joseph	Pune, Maharashtra, India
16. Xander Graff	Delta High School, Delta, Colorado
17. Anika Flores	Central High School, Grand Junction, Colorado
18. Yaneli Arevalos	Central High School, Grand Junction, Colorado

Send any comments or questions to: David Pleacher