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 = 123The 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 |