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Can you solve the cheating royal riddle? - Dan Katz


4,482 Questions Answered

TEDEd Animation

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You’re the chief advisor to an eccentric king who needs to declare his successor. He wants his heir to be good at arithmetic, lucky, and above all else, honest. So he’s devised a competition to test his children, and ordered you to choose the winner. The future of the kingdom is in your hands. Can you find the worthiest successor? Dan Katz shows how.

Additional Resources for you to Explore

A king wants to choose his successor using a dice-rolling contest where the best total wins. But with the contestants rolling behind closed doors, the highest score may not be legitimate. Can you assess the results with mathematics and ensure that the new ruler will be an honest one?This lesson explores two different areas of mathematics: probability and number theory.Probability is the study of the likelihood of random events. If you roll one fair six-sided die, every face should land on top one-sixth of the time. If you assume every roll is independent, probability tells us that the chance of multiple events happening can be calculated by multiplying the individual probabilities together.The reasoning behind Cassandra’s disqualification relies on the extremely low probability of rolling the single highest number 40 times. Ruling out possibilities based on their extreme unlikelihood is the basis of hypothesis testing in statistics.Number theory is the study of integers and their properties. One of the first topics in most introductory number theory courses is modular arithmetic, the idea that if we divide all integers by a particular number or “modulus,” there are addition and multiplication rules for the remainders.The reasoning behind Draco’s disqualification relies on the fact that 3 + 2 = 0 “modulo 5,” and so the sum of two numbers with remainders of 3 and 2 after dividing by 5 will always have a remainder of 0 after dividing by 5.If you’d like to explore modular arithmetic further, experiment with what happens if you divide a lot of square numbers (the result of multiplying integers by themselves) by 5. What remainders occur, and what remainders never seem to occur? Can you figure out why this happens?

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TED-Ed Animations feature the words and ideas of educators brought to life by professional animators. Are you an educator or animator interested in creating a TED-Ed Animation? Nominate yourself here »

Meet The Creators

  • Educator Dan Katz
  • Director Igor Coric
  • Narrator Addison Anderson
  • Animator Igor Coric
  • Storyboard Artist Igor Coric
  • Compositor Igor Coric
  • Art Director Igor Coric
  • Director of Production Gerta Xhelo
  • Editorial Director Alex Rosenthal
  • Producer Bethany Cutmore-Scott
  • Fact-Checker Eden Girma

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