Need help with another student math challenge
I asked for help on one of my student's math challenges a few weeks ago, and you guys delivered. I'm a middle school gifted support teacher / hobbyist programmer, and we do some Scratch and basic Python in class.
This week's problem involves placing coins on a grid so the rows, columns, and diagonals each equal a given value. My student finished the problem using pencil/paper/logic, but we still want to solve it with a program.
Of course, we're not exactly sure how to approach it since though there are restrictions, there are also multiple options.
# Put the values of nickels (5), dimes (10), and quarters (25) on certain # sqaures of this grid. Observe the following rules while doing so: # # Rule 1 - Only one coin per square # Rule 2 - The rows must add up to equal the values on the right # Rule 3 - The columns must add up to equal the values on the bottom # Rule 4 - The diagonals must add up to equal the value at the corners # Rule 5 - Put the value of each coin in the box # # Several coins have already been placed to help get you started. # The box with a star is to remain blank. # Hint: Not every square needs to have a coin. Some will remain blank. # # 40 55 # +--+--+--+--+--+ # | |10| | | | 40 # +--+--+--+--+--+ # | | | |S | | 15 # +--+--+--+--+--+ # | | | | | | 85 # +--+--+--+--+--+ # | |25| | | | 65 # +--+--+--+--+--+ # |10| 5| 5| | | 40 # +--+--+--+--+--+ # 60 65 40 45 35 #
View the game board here: https://drive.google.com/file/d/0B2mj8hA_IkqCV2xqcE9pTk5lLWc/view?usp=sharing
Online editor: https://repl.it/E1Oe/2
Thanks in advance!