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Explain how the counting problem above can be modeled with strings of length 16 from the alphabet {L,U}. Give mathematical formu- lations of both bullet points above using these strings. Use this formulation in your proofs of the next parts. and find the number of ways for the lion and the unicorn to eat the cake where they both eat the same number of pieces.

Explain how the counting problem above can be modeled with strings of length 16 from the alphabet {L,U}. Give mathematical formu- lations of both bullet points above using these strings. Use this formulation in your proofs of the next parts. and find the number of ways for the lion and the unicorn to eat the cake where they both eat the same number of pieces.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 33EQ
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Explain how the counting problem above can be modeled with strings of length 16 from the alphabet {L,U}. Give mathematical formu- lations of both bullet points above using these strings. Use this formulation in your proofs of the next parts. and find the number of ways for the lion and the unicorn to eat the cake where they both eat the same number of pieces.

Question 2 The lion and the unicorn were fighting for the crown. A lion and a unicorn are having a plum cake eating competition. They start with a plum cake divided into 16 identical pieces. In this exercise, you will count the number of ways for the lion and the unicorn to eat the cake so that • they both eat the same number of pieces and • at any point while they are eating the lion has always eaten at least as many pieces of cake as the unicorn. Note: It is the order in which they eat the pieces that matters. For instance, if they just alternate 1 piece at a time (Lion eats one, unicorn eats one, etc) then that is different from the lion eating all his 8 pieces first and the unicorn eating his 8 afterward.
Transcribed Image Text:Question 2 The lion and the unicorn were fighting for the crown. A lion and a unicorn are having a plum cake eating competition. They start with a plum cake divided into 16 identical pieces. In this exercise, you will count the number of ways for the lion and the unicorn to eat the cake so that • they both eat the same number of pieces and • at any point while they are eating the lion has always eaten at least as many pieces of cake as the unicorn. Note: It is the order in which they eat the pieces that matters. For instance, if they just alternate 1 piece at a time (Lion eats one, unicorn eats one, etc) then that is different from the lion eating all his 8 pieces first and the unicorn eating his 8 afterward.
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