The first thought for a title was not so good: "An Orthogonal Approach to Problem-Solving." Glad I dropped “orthogonal”...
Getting back on track. To drive radical change it helps if you are able to look at problems from a different perspective. I do not mean gathering diverse opinion. That can be helpful. But what change is needed is for you to approach things at right angles. To train your own mind to break out of set patterns. To open yourself up to learn. Overcome built in bias.
One great way to develop this is to study riddles. And more specifically to see where you get stuck. Or where others get stuck. In doing so you can learn the pitfalls. Mostly these are “thought ruts”. Like ruts in the road they are set patterns. Patterns that keep you fixated on one option. When you recognize this you can elevate your thinking to a new level.
Here is an example that I have always enjoyed. I was first told it at a company retreat in my first few months of full time employment. It goes something like this:
The POW Puzzle
Four prisoners of war have escaped from a German POW camp (I was told this in England but you can change the key parts for any situation). They have fled down the hill to a bridge. Over the river is freedom. It is a dark night and the bridge has been damaged. On the bridge they have to be careful where they step. Prior injuries mean they each walk at different speeds. Also they only have one source of light: A torch (or flashlight for US English). And to make things worse, the prison guards are coming. To get safely across they can only travel two at a time, and carry the torch back and forth. Someone has to return to with the torch so that two can cross.
The other piece of information you need is travel time for each escapee. On their own they take, 1, 2, 5 and 10 minutes to cross the bridge. How long do they need to get to the other side of the bridge safely before the guards get there? It makes it more interesting if you have people give their answers individually (such as writing on paper) rather than shout it out.
(This is a good opportunity to try out the puzzle for yourself before I reveal the answer.)
How People React to the Big Reveal
When you ask this riddle most people will quickly come to an answer. Often it will be 19 minutes. When you tell them they are wrong you will get two responses. Digging in to explain why they’re right, or an attempt to approach it from a new perspective. Digging in means some pain. Curiosity can lead to a different outcome.
The typical approach is to assume that two people cross the bridge and then one comes back. The fastest return journey is to send the 1-minute person across with someone and then have the “1” return. You do this each time and you get 2+1+5+1+10 which is 19 minutes. People get into the rut that the fastest person needs to return the torch to then guide the next person across.
Tell them that it is not the right answer and let them think. You can then always tell them the answer but they need to explain it. Don't give in too quick. Or the learning will be lost.
If you let go of this mental construct that the fastest person always returns the torch you can figure out that the key is to get the two slowest to walk together and only cross once. Now you can come up with a winning option. 2+2+10+1+2 which is 17 minutes (and some similar permutations). If you can’t break out of this rut you will suffer with this puzzle for a long time.
Try it with a group and see what happens.
Next time you end up in a rut with a problem, ask yourself what assumption am I making that is critical, and what would happen if I just ignored it.