Answer to November 22, 2004 Problem
by Dr. Alexander Bogomolny

Chocolate Squares

If you have a chocolate bar consisting of squares arranged in a rectangular pattern -- say 2 x 5 squares. Your task is to split the bar into small 1 x 1 squares (always breaking along the lines between the squares) with a minimum number of breaks (you may not lift up pieces and place them on top of each other).

How many breaks will it take to break up a 2 x 5 chocolate bar into 1 x 1 squares?
If the chocolate bar has m row by n columns, what is the minimum number of breaks needed to split it into 1 x 1 squares?

 


Solution to the Problem:

The answer is 9 breaks for the 2 x 5 bar and (m) (n) - 1 for the m x n bar. It always takes one less than the number of chocolate squares.

Click here for a demonstration.

Click here for a puzzle about chocolate math!


Correctly solved by:

1. Tristan Collins Winchester, Virginia
2. Walt Arrison Philadelphia, Pennsylvania
3. Emily Auerbach Columbus, Georgia
4. Mandy Auerbach Columbus, Georgia
5. Keith Mealy Cincinnati, Ohio
6. James Alarie University of Michigan -- Flint,
Flint, Michigan
7. Tyler Windham Columbus, Georgia
8. John Funk Ventura, California
9. Dave Smith Toledo, Ohio
10. Jason LaRusso Winchester, Virginia
11. Cameron S. Columbus, Georgia
12. Jim Kennedy Limerick, Ireland
13. Arin Smith Winchester, Virginia
14. Jeffrey Gaither Winchester, Virginia
15. Jaime Garcia-Ramirez Virginia Tech,
Blacksburg, Virginia
16. John Beasley Lord Fairfax Community College,
Middletown, Virginia
17. David & Judy Dixon Bennettsville, South Carolina
18. Jonas Sutinen Tullängsskolan, Hällefors, Sweden
19. Anders Johansson Tullängsskolan, Örebro, Sweden
20. Per Björkil Tullängsskolan, Örebro, Sweden
21. Tobias Flodmark Tullängsskolan, Örebro, Sweden
22. Gustav Nilsson Tullängsskolan, Örebro, Sweden
23. Erik Hultgren Tullängskolan, Örebro, Sweden
24. Jonathan Jansson Örebro, Tullängensskola, Sweden
25. Joakim Berggren Örebro, Tullängskolan, Sweden
26. Stehr Ako Örebro, Tullängskolan, Sweden
27. Erik Ekman Örebro, Tullängskolan, Sweden
28. Joanna Sturk Örebro, Tullängsskolan, Sweden
29. Lisa Sevón Örebro, Tullängskolan, Sweden
30. Niclas Andersson, Sebastian Jacobson, Andreas Börjesson Örebro, Tullängskolan, Sweden
31. David Hedberg Örebro, Tullängsskolan, Sweden
32. Bahadir Güngör Örebro, Tullängskolan, Sweden