Batch 3 - Class 189 - World's Greatest Detective

Pre-Class Exercise

(536Dudeney - 319) The fly at point A below take a minute to crawl an edge of the cube. How long will it take it to reach point B?

Attendance Kushagra, Anshi, Siddhant, Rhea, Rehaan, Mahi, Arjun, Arnav, Rohan, Damini, Aashvi, Liza, Smiti, Muskaan

Class puzzles

Today's puzzles are taken from https://www.nytimes.com/2016/09/19/crosswords/loh-detective.html - Not being reproduced here for sake of brevity.

Answers and approach:

The Demise of Mr Gibson

One can solve this problem with pure logic – kids may do that
The other way to look at this is a bipartite graph. A bipartite graph can only have even-length cycles. In this case, we see two odd length cycles, but with only one common edge between those cycles. Hence the person claiming that edge must be the liar, and hence the murderer (B)

The Dastardly Crime

One can draw an “implication graph”, i.e. what are the implications in the statements.

Kids may have some difficulty writing the third implication (if D, then E=>A)
Now if D is guilty, you have a long cycle, which means either everyone else is guilty or everyone else is innocent. That means D can’t be guilty – this gives us a guilt chain, and only the last two of those can be guilty (otherwise there will be more than two guilty),i.e. B & E.

The Very Odd Island

This is a parity problem, and a harder one.
Kids will have to work to first reason the number of liars, depending on what those configurations can be, and how many people would claim odd/even in those cases. Note that liars will lie about even/odd reporting

One way to solve this is in binary arithmetic – 1 representing liar, and 0 representing truthteller. Now, for example A+C+F+G+H should be odd (if A is liar and is reporting odd, which should actually be even; or if A is telling the truth and reporting odd), and so on. You get a system of 8 linear equations, which can be solved to determine that A,C,G,H are truthtellers.

If kids want to solve for a easier problem, allow them to solve for a pentagon (system of five equations in five variables), say answers successively being OOEOO, in which case first and last happen to be the liars.

Homework Problem:

(536Dudeney - 324) A squirrel goes spirally up a cylindrical pole, making a circuit in four feet. How many feet does it travel to the top if the post is sixteen feet high and three feet in circumference.

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