Can you replace the letters A, B, C, D, E, and F with positive, single-digit, non-zero numbers so that each circle contains the same total?



 

Solution to Problem:

A = 5
B = 4
C = 5
D = 1
E = 7
F = 8

To get started, look at the top left circle and the top middle circle.
The top left circle contains A, 7, and 8 while the top middle circle contains A, 8, B, and 3.
Since each circle must contain the same sum,
A + 7 + 8 = A + 8 + B + 3.
Subtracting A + 8 from each side, we obtain
7 = B + 3. Therefore, B =4.
Look at the two circles below these.
It can be seen that D must equal 1.
This gives you the sum of each circle (20).
Now you can solve for A and continue around the circles.



Correctly solved by:

1. Richard K. Johnson La Jolla, California
2. Rick Jones Kennett Square, Pennsylvania
3. Renata Sommerville Austin, Texas
4. Keith Mealy Cincinnati, Ohio
5. Justin Collins Winchester, Virginia
6. John Funk Ventura, California
7. Griffin ----------
8. Christopher March Virginia Tech, Blacksburg, Virginia
9. David Powell Winchester, Virginia
10. Vanessa Kargenian Rockford, Michigan
11. Tori Eads Winchester, Virginia
12. George Gaither Winchester, Virginia
13. Izzy Kushner Closter, New Jersey
14. Matt McMurtry Arlington, Virginia
15. James Alarie University of Michigan -- Flint, Michigan
16. Geoff Keith Santa Monica, California
17. Josh Grewal College of William and Mary, Williamsburg, Virginia
18. Amy Lamport Rockford, Michigan
19. Sarah Jarrell Columbus, Georgia
20. Jonathan Pence Virginia Tech, Blacksburg, Virgina
21. Walt Arrison Philadelphia, Pennsylvania
22. Rob Maccubbin Alexandria, Virginia
23. Andrea Flandry Columbus, Georgia
24. Dave Marut Old Dominion University, Norfolk, Virginia
25. Ann Conger Columbus, Georgia
26. Mulford Waldrop Columbus, Georgia
27. David and Judy Dixon Bennettsville, South Carolina
28. Robert Calhoun Columbus, Georgia