The Essentials of Problem Solving

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16:10 HOOOOLY SHIT, i feel tricked... the way you imbued this in the video 😂, everything follow a progression. I was predicted so well i feel toyed, i think i correctively thought that my lack of math skills were preventing seeing other possibilities, i was so caught up in the number and i didnt think the last was a calculus.

11:50 I feel this is more about the incremental problem cause if you never see the box as an option you will keep blind till the very end or think that using it is wrong like in the case that math formula students. Thats the thing that really hit me, to make the invisible visible and not feel youre cheating or the unknown risks of a jerryig, i think many times we - or at least i - dont dare to improvise due to tapping in unknown areas (i really wish i had studied engineering and science growing up, i really really wish, we are our tools but our mindset its to buy them. But what am saying? People would find a way to ruin it anyway, just like with that candle problem, we had good materials but we were trying to stick the candle with the pins)

7:02 No matter what you choose 1 its gonna be unturned which can invalidade this

7:43 Sounds the same but its a false analogy

8:43 Yeah, but wonders if EVERY card has, not if the 1st and 4rd cards have it

on the roman numerals problem, my "solution" was to move any stick over the equal sign to make it be a not equal sign. mic drop 🤚🎤

I would say the toothpick problems were not much about insight. More about trying random combinations until it works. It's really about trying mamy different moves. Its a single move from problem to solution. Unlike the candle on the wall problem.

13:40 I moved the vertical stick on the "+" to make it: XI ≠ III - III

GOAT VIDEO ❤❤❤ Watching this again for 4th time 🔥🔥🔥

https://www.youtube.com/watch?v=6DxTQiJuAoc

#st/source

You start with
"The Starting State"

The Problemsolver can perform different operation to move into another Problem State

In the End you have to achieve "The Goal State

What means State-Space?
Problem-State-Space describes all the different Problem-States and the Operation to move in between:
Exp: Problem State-Space of Tower of Hanoi
![[Pasted image 20240407184927.png]]

<mark style="background: #BBFABBA6;">The Difficulty of Problem is partially through the Complexity of the Problem-State-Space
</mark>

Exp.: Chinese-Ring-Puzzle
There are only 22 State-Spaces and you can either get closer to the goal space or redo the previous move (means the state space ist linear)
![[Pasted image 20240407185445.png]]
The Difficulty here is, to see the state, there are in. And to figure out how to effectively move from one state to another state.
<mark style="background: #BBFABBA6;">If you visualize the state's you are in more clearly</mark> maybe through a computer simulation programm people are much more likely to solve this chinese ring puzzle.
The means:
<mark style="background: #BBFABBA6;">"Problem-solving is not just about the nature of the Problem"
</mark>

<mark style="background: #BBFABBA6;">How we navigate through the problem space depends on how we interpret the problem space </mark>
M: So Visualizing is part of the Interpretation of the problem space

Exp: Watson 4 Card test vs pretty similiar Test vor (9:34)
M: The pretty similiar test is played with more familiar rules
These 2 Tests are the same problem even the same problem-state-space but with different Contexts, but people tend to solve the second Test much better than the Watson 4 Card Test.
Result: <mark style="background: #BBFABBA6;">The Context can change how we think about the Problem, even if the Problem is the same
</mark>

Sum von Doc:
1. Complexity of the Problem
2. Interpretation of the Problem (and therfore Visualization of the Problem)
3. Context of a Problem
influence the Difficulty of a Problem

Sum featuring my thouhgts:
Know the Goal State
Understand in which state you are by visualizing your state.
Try to figure out how to effectively change states.
# Part 2
Insight Problems:
Exp: The Puzzle with Candle, box with Stecknadeln, Streichholzpackung mit Streichholz
The Problem here is to realize not just the Stecknadeln, Streichhölzer and Candle as Tools, but the Box as well.

Differenzce between Insight Problem and Incremental Problem (the Examples before):
In Incremental Problems, you know when you get closer to the goal state. At Insight Problems you're not.

2 Barriers to insight:
Exp: Roman Stick Problem:
![[Pasted image 20240407193916.png]]
You could possible perceive the representation of a 4 as a chunk.
But you can change it to I and V and recombine to VI.
<mark style="background: #BBFABBA6;">
Sometimes we have Problems to travel between different Levels of a Chunk</mark>
You have to decompose a chunk, and then try to solve it.

Contraints = Intial Representation of the Problem, does implicit a not given assumption
![[Pasted image 20240407194707.png]]
Bisher mussten wir Zahlen verändern (und man könnte annehmen, dass muss man hier immernoch machen), aber eig. muss man hier die Operatoren ändern.

Mental Set = If you solve a number of problems with the same approach succesfully, but then there does come up another problem, which requires a different approach, your ability to see a different approach is impaired

Most realistic Problems: require both incremental and insight.

# Part 3 Wellstructured vs ill-structured Problems
All Exp before were wellstructured
Most realistic Problems are ill-structured:
Exp: Klimate change, sending man to mars, providing cheap but reliable public transportation

The Lessons of well-structured problems still apply to ill-structured problems:
we still have to look for alternatives and evaluate, which

As a physicist I am gonna quote Albert Einstein: "I agree"
P.S.: Really cool video

awesome quotes from the end of the video:
- "to solve hard problems requires you learn while solving the problem"
- "if you don't have to learn anything, while solving a problem, what you are doing is performing an exercise, its not fundamentally a problem for you, because you already know how to do it."

Can you make this 1 hour video we need more insights - examples - application ❤

GOAT VIDEO 🔥🔥🔥

What I did for the roman matchstick problem was remove the vertical matchstick in the plus symbol and adding it to the first III making a seven, so VII - III = IV. Or does twisting one of the matchsticks to make a V shape violate the rules?

You look like Buck from Halo ODST (just skinnier).
Btw, i love your video

Now i wonder if this id what the use of leetcode is for

Thank you for share!

Nice video, Really Found it helpful ❤

hi friends, with all respect, i dont think the approach to solving matches problem is good. We notice that there ares 17 matches, and removing 5 leaves us with 12, so for 12 to creaate total 3 squares, all of the 3 must not share the same line. So we can just choose 3 separete squares and removes the other 5. Thanks for reading. Come back. I miss the core ideas. thanks for the teaching.

Hello Benjamin. Do you have any video about programming/problem solving? How do some people get really good at while other dont

Without conditions, there are multiple cases or states.
With conditions, those states or cases will be reduced to a certain number.

Bro had to put his PhD in the name of the channel 😂