Answer to February 19, 2001 Problem

From Loren Krienke
in Recreational & Educational Computing Vol. 14, No. 3

The Gold Bags Problem

 
Notorious bandit Clark Sherando was counting the 7 bags of gold coins he had just acquired from holding up the Gore Stagecoach. One bag had 10 coins, another 20 coins, and so on in increments of 10 coins up to 70.

His bandit brother Jimmy Wood rode up on a horse and demanded the 3 bags with the most coins.

Sherando labeled the bags A to G and informed Jimmy that he could have the three biggest bags if he could work out which they were from these simple facts:

Bags B, D, E, and G contain a total of 150 coins.
Bags A, C, D, and E had 100 coins.
Bags A, B, D, and F had 170 coins.

Which three bags should Jimmy take?

 

Solution to Problem:

Jimmy should take bags B, F, and G.

In order for 4 bags to add up to 100, they must be 10, 20, 30, and 40. So from clue #2, these must be bags A, C, D, and E.
Thus the remaining bags must contain 50, 60, and 70.
So, take bags B, F, and G.

However, not everyone was content to just answer the question. Ronald D. Morton, Stan Winston, and Jeannette Scofield sought to determine the contents of each of the 7 bags:

There are four possibilities which satisfy the initial constraints:

 A    B    C    D    E    F    G
---  ---  ---  ---  ---  ---  ---
 20   50   40   30   10   70   60
 30   70   40   10   20   60   50
 40   50   20   10   30   70   60
 40   50   30   20   10   60   70


Correctly solved by:

1. Ryan Throckmorton Winchester, Virginia
2. George Gaither Winchester, Virginia
3. David Powell Winchester, Virginia
4. Simmonds ----------
5. Mark Fenster Dayton, Ohio
6. Kurt Fischer Joliet, Illinois
7. Louis Farrell Kimberley, South Africa
8. David Dixon Bennettsville, South Carolina
9. Gadi Manor ----------
10. Steve Stermer Colorado Springs, Colorado
11. Joe Heintz Manchester, Tennessee
12. James Alarie University of Michigan -- Flint
13. Shawn Bercovitch ----------
14. LouAnn Dossett Russellville, Alabama
15. Don Dunsmore Maryland
16. Karen Russell ----------
17. Norman Santora ----------
18. Gary Armstrong Athens, Greece
19. David Jacobson Houston, Texas
20. Mike Howard Sunrise, Florida
21. Ron Morton Pittsburgh, PA
22. Bill Hall Wellington, Florida
23. Tom Adams ----------
24. Jackie ----------
25. Barb ----------
26. Richard Johnson La Jolla, California
27. Mark Kantrowitz ----------
28. Erin McGinnis Winchester, Virginia
29. Sasha Joseph Hebron, Maine
30. Stan Winston ----------
31. Jim Kennedy Limerick, Ireland
32. Jim Netter Chicago, Illinois
33. Kate Grumbacher Alexandria, Virginia
34. Kirstine Wynn Winchester, Virginia
35. Walt Arrison Philadelphia, PA
36. Josh Stock Wheaton College
37. Jeannette Scofield Novato, California