Discrete Math - 1.2.2 Solving Logic Puzzles

In this video we talk about strategies for solving logic puzzles by reasoning and truth tables.

Video Chapters:
Intro 0:00
Knights and Knaves Using Propositions 0:10
Knights and Knaves Using a Truth Table 4:57
Party Planning Practice 9:15
Up Next 16:02

Textbook: Rosen, Discrete Mathematics and Its Applications, 7e

[taulguedi]

This puzzle haunted me for years. With a paper and a little bit of patience I solved it for myself. (Maybe that is childish but... I am so proud!). :)) Thank you for the class. You have a new student.

[Orengelol]

Kimberly you greatly assisted me in Linear Algebra, now you're assisting in Discrete! Thank you for your videos

[sabrinanastasi]

The best videos on discrete math on the internet and outside the internet. Thank you!

[briwitbeck]

I am simultaneously taking Discrete Math and Linear Algebra and your courses are helping me immensely. I need online coursework as an ADHD person. In person classes are killing me and you have saved my GPA.

[johnathanrhoades]

I love the party planning. It’s like “or, of course, you could just not have a party in the first place!” 😂

[caitlindominguez]

I am so thankful I stumbled across your channel. I am in a discrete math class for computer engineering and I am in a different country so I'm learning it in my second language. I am so thankful I have some help in English now.

[aryamhaske]

"Y'all need to grow up and don't invite any of them" I'm dying😂😂 literally most of the time this happens. Awesome Lecture! Thank You for a wonderful exercise with great explanation!

[GFh-vw]

Thank you so much, Miss Brehm for your very helpful tutorials. At first when taking my classes, nothing made sense, but you are breaking it down and making it much easier for me to understand it. Amazing work and I will continue to watch all your videos to comprehend what I am learning.

[alex-nblh]

it would be nice if you elaborated on your reasoning while filling out the truth table in the three friends problem, it is difficult to follow

[brunilda]

For the knights and knaves puzzle there is a really easy, really cool algebraic method (essentially algebra in the Galois field modulo 2, where the only numbers are 0 and 1, and 1+1=0). We use 0 to represent "false" and 1 for true; then you translate A says "B is a knight" by (A is a knave) + (B is a knight) = 1
(Why? Because is "A is a knave" is true, equal to 1, then "B is a knight" has to be false, equal to 0 to make the equation true; conversely, if "A is a knave" is false, then equal to 0, in order to make the equation true "B is a knight" has to be 1, that is true. Note that p+q=1 is an algebraic translation of p XOR q.)
The second statement is (B is a knave) + (A is a knave XOR B is a knave) = 1, that is, (B is a knave) + (A is a knave) + (B is a knave) = 1. Because adding the same thing to itself in GF2 is 0, the second equation resolves to "A is a knave" = 1. From that, plugging in the first equation, "B is a knight" has to be 0, so B is also a knave.
Once you understand how this works, a complete solution looks simply like this (with T for knight and F for Knave):
1. A is F + B is T =1
2. B is F + (A is F + B is F) = 1
From 2, A is F = 1; therefore, replacing in 1 + B is T = 1, so B is T = 0.

[saiefshamsmurad]

15:56 DON'T INVITE ANYONE!!! Simplest solution ever (assuming that then they won't be "unhappy" with me )

[spencerjames]

I wish I could've had you a professor

[kristoffercorbyn]

My preferred approach to the truth table for knights and knaves is by making each column and explicit logical statement that you can plug in the truth values into, all building up to the final conclusion in the last column. Like: (A), (B), (A<->B), (A XOR B), (B<->(A XOR B)), [(A<->B) ^ (B<->(A XOR B))].

Setting up the biconditionals effectively sorts out the truth of their claims accounting for their state as a knight or knave. That way it's all really straight forward plugging in T/F with no thinking involved.

[sunnyzhu]

American will be great again. Before that, everyone should come here to learn from professor Kimberly Brehm

[awmirrzza]

That was the best video I've ever seen in terms of Island Of Liars&Truth Speakers. I just wish you could also go through some more examples in terms of these kinda questions:)

[TheAngryMaskSalesman]

Bob Ross of Discrete Math. Thank you for these videos!

[DANKAF]

you dont need to fill the table, you can directly eliminate from the possibilities, for example, if you find j -- >s eliminate / if you find s -- > not k eliminate / if you find k -- > not j eliminate. ull end up with the same results without filling all that table

[RenaudAlly]

Commenting here so I can hopefully come back to this video. I'm still confused on how to translate sentences to implication propositions (difference between "if" and "only if")

[csjoy]

thanks for your explanation, mam. now, I got understand the idea of logic puzzle. I am a student in computer science and engineering. You got an student.

from Bangladesh

[mackenzielewis]

your videos are extremely helpful! thank you so much for making these