Good Math Riddles: Find Fun Challenges Here

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Discussion Overview

The discussion revolves around finding and sharing math riddles, specifically focusing on a cake-sharing problem involving multiple participants. The scope includes conceptual exploration of fair division and mathematical reasoning related to the proposed riddle.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant requests a site for good math riddles.
  • Another participant suggests using Google to find math riddles but notes that their experience with one site was unsatisfactory.
  • A participant presents a cake-sharing riddle and asks for a solution applicable to an arbitrary number of people.
  • One response questions the effectiveness of the proposed cake-sharing method, suggesting that it does not guarantee equal shares but rather fairness in perception.
  • A detailed procedure for sharing the cake among multiple people is proposed, emphasizing that everyone must believe they received a fair portion.
  • Another participant argues that the original cake-sharing method does not work as intended, providing a personal example to illustrate their point.

Areas of Agreement / Disagreement

Participants express differing views on the effectiveness of the proposed cake-sharing method, with some agreeing on the need for fairness in perception while others challenge the method's validity. The discussion remains unresolved regarding the best approach to ensure fair sharing among multiple participants.

Contextual Notes

The discussion includes assumptions about participants' desires for larger portions and the implications of fairness in cake-sharing. There are also unresolved aspects regarding the mathematical rigor of the proposed solutions.

daniel_i_l
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Does anyone know a site where I can find good math riddles?
Thanks.
 
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daniel_i_l said:
Does anyone know a site where I can find good math riddles?
Thanks.
Google math riddles, and you'll get a bunch. I only looked at one though and it wasn't good.
 
Here's one:

There is a simple procedure that ensure two people share in equal part a cake: one person cuts the cake, and the second chooses his/her piece first. What procedure should be taken for an arbitrary number of persons?
 
the cutter always gets the last piece?
 
Werg22 said:
There is a simple procedure that ensure two people share in equal part a cake: one person cuts the cake, and the second chooses his/her piece first. What procedure should be taken for an arbitrary number of persons?

This question is incorrectly stated, but I think I understand what you're asking. It won't ensure that people get an *equal* share-- it ensures that neither person is justified in thinking that they got an unfairly small amount of cake, assuming that each finds larger portions desirable.

But anyway, a solution to the arbitrary number of people would be:

A) Nth person cuts a piece from "the cake".
B) The piece is passed to the next person, who may further subdivide the piece if he/she wishes.
C) If the piece is subdivided further, excess is returned to "the cake"
D) Repeat steps B & C until each person (apart from the Nth) who does not already have a piece of cake has had the option to subdivide the piece.
E) Whoever was the last person to cut or subdivide the piece is given that piece.
F) Repeat steps A-E until only 1 person does not have a piece of cake, who is given the remainder of the cake.

This ensures that assuming everyone wants as large a piece as possible, that everyone has a portion that they must think (or must have thought) was fair, and is therefore unjustified in thinking is anything but fair.
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DaveE
 
Werg22 said:
There is a simple procedure that ensure two people share in equal part a cake: one person cuts the cake, and the second chooses his/her piece first.
It doesn't work. If I cut some tasty morsel in two to share with my wife, if one piece is larger than the other, I give her the larger piece. If I give her a choice she will invariably choose the smaller.
 

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