What is the first puzzle in MHB's puzzle contest?

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    Contest Puzzle
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Discussion Overview

This thread focuses on a series of puzzles presented by participants, inviting others to solve them and contribute their own. The puzzles range from logical reasoning to probability and combinatorial challenges, emphasizing creative thinking rather than extensive computations or advanced mathematics.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • The first puzzle involves determining the positions of three individuals based on given clues about their earnings and relationships.
  • One participant proposes a probability puzzle involving two coins, asking for the likelihood that the other side is heads given that one side shows heads.
  • Another participant presents a riddle about antique clocks, questioning which clock would show the correct time most often.
  • A subsequent puzzle challenges participants to correctly label three boxes based on the information gained from removing a single item from one box.
  • Another puzzle involves measuring exactly four gallons of water using a five-gallon and a three-gallon jug.
  • Lastly, a digit puzzle is introduced, where letters represent digits, and participants are tasked with finding the corresponding digits.

Areas of Agreement / Disagreement

Participants engage in discussions that involve multiple interpretations and solutions to the puzzles, with some participants agreeing on methods while others propose alternative approaches. The discussion remains unresolved on certain puzzles, as participants explore different reasoning paths.

Contextual Notes

Some puzzles may require assumptions or specific interpretations that are not universally agreed upon, leading to varying solutions and methods of reasoning.

Who May Find This Useful

Individuals interested in logical reasoning, probability puzzles, and creative problem-solving may find this thread engaging and stimulating.

  • #31
$$1^2-0^2=1^3$$
$$1^3-0^3=1^2$$
 
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  • #32
mathworker said:
$$1^2-0^2=1^3$$
$$1^3-0^3=1^2$$

In some context 0 is not a whole number ;) .
 
  • #33
  • $$10^2-6^2 = 4^3 $$
  • $$10^3-6^3 = 28^2 $$
 

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