Integer Programming: Solving a Puzzle with Excel Solver

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If you are not familiar with the concept of binary variables and logical constraints, I recommend you watch these two videos first:

In this video I decided to do something different and illustrate how to use binary variables to solve a fun puzzle. It is a nice exercise to practice the concepts of yes/no (binary) decisions and logical conditions. This spreadsheet also works as a tool to help you create your own (maybe larger) versions of this puzzle to play with your friends. Enjoy!

[daniellebenjamin]

Really cool. I'm trying to solve a problem with multiple constraints... I'm spinning my wheels!

[yja]

Very cool model and teaching idea!
Interesting that the constraints can be modeled in multiple ways; for example, I came up with this for the 206 hint:
X22 + X23 + X01 + X03 + X61 + X62 = 2 (Xij where i = digit, j= position)

[stevemansfield]

Great stuff. I set up my own version, predefining a solution, then writing "Hints" that conformed to the solution, set up all the rest of the model and ran SOlver. It found a solution but not my solution! As a general question, is there a way of getting Solver to show all possible solutions and if so how do you do that? Or will it just stop at the first solution it finds?