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)
Hi Yousef! Nice to see you around here. You're right that there are alternative ways to write the constraints, which is interesting for the students to see.
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?
There's no way to ask Solver to show all solutions. One way to look for other alternative solutions to a problem is to first solve it, then force the current solution to change by adding a constraint (e.g. forcing a binary variable that is currently at 0 to become 1, or vice-versa), then solve again. If the objective value stays the same, it means you've found an alternative optimal solution (same value, different course of action). You can then repeat this by modifying other variables. This won't necessarily find all alternative solutions (if you modify one variable at a time), but will find some. Other commercial packages for optimization (not Excel-based) will pre compute alternative optimal solutions and will show them upon request.
Really cool. I'm trying to solve a problem with multiple constraints... I'm spinning my wheels!
Take a look at my "Excel Models" playlist. There's a good chance the one you're trying to solve is similar to a problem I address in there.
Excellent.
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)
Hi Yousef! Nice to see you around here. You're right that there are alternative ways to write the constraints, which is interesting for the students to see.
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?
There's no way to ask Solver to show all solutions. One way to look for other alternative solutions to a problem is to first solve it, then force the current solution to change by adding a constraint (e.g. forcing a binary variable that is currently at 0 to become 1, or vice-versa), then solve again. If the objective value stays the same, it means you've found an alternative optimal solution (same value, different course of action). You can then repeat this by modifying other variables. This won't necessarily find all alternative solutions (if you modify one variable at a time), but will find some. Other commercial packages for optimization (not Excel-based) will pre compute alternative optimal solutions and will show them upon request.