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Error detection Lying once Error Correction Gold and Pirates Class Quiz Campus Challenge: Brain Games STUDYSmarter, UWA Adrian Dudek

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Page 1: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Campus Challenge: Brain GamesSTUDYSmarter, UWA

Adrian Dudek

Page 2: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Information

Every development in modern technology relies on a new way of storing,exchanging and presenting information.

• Television• The Internet• Mobile Phones

Of course, we live in a time whereall three of these appear in a singledevice!

Page 3: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Reliable InformationWhen you send an SMS to somebody ...

... your message gets turned into a string of 0’s and 1’s before it gets sentout. This string hits their phone and gets translated back to English.

“I love you”⇒“01001001001000000110110001101111011101100110010100100000011110010110111101110101

⇒ “I love you”

“I love you”⇒ERROR

“01001001001000000110110001101111011101100110010100100000011111000110111101101101

⇒ “I love tom”

Page 4: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Reliable InformationWhen you send an SMS to somebody ...

... your message gets turned into a string of 0’s and 1’s before it gets sentout. This string hits their phone and gets translated back to English.

“I love you”⇒“01001001001000000110110001101111011101100110010100100000011110010110111101110101

⇒ “I love you”

“I love you”⇒ERROR

“01001001001000000110110001101111011101100110010100100000011111000110111101101101

⇒ “I love tom”

Page 5: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Reliable InformationWhen you send an SMS to somebody ...

... your message gets turned into a string of 0’s and 1’s before it gets sentout. This string hits their phone and gets translated back to English.

“I love you”⇒“01001001001000000110110001101111011101100110010100100000011110010110111101110101

⇒ “I love you”

“I love you”⇒ERROR

“01001001001000000110110001101111011101100110010100100000011111000110111101101101

⇒ “I love tom”

Page 6: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Detecting errors in messagesBar codes, ISBN numbers and Credit cards

• What happens when you are buying apple juice in the supermarket,but there is a mistake on the bar code?

• Thanks to mathematics, supermarket bar codes are a reliable andsafe way to label supermarket items.

Page 7: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Detecting errors in messagesBar codes, ISBN numbers and Credit cards

• What happens when you are buying apple juice in the supermarket,but there is a mistake on the bar code?

• Thanks to mathematics, supermarket bar codes are a reliable andsafe way to label supermarket items.

Page 8: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Activity 1: Checking Barcodes

Checking for an error in the code

• There are 13 numbers, the last is the check digit.

• Add up the numbers in the odd places (1st, 3rd, 5th, 7th, 9th, 11th)and multiply by 3.

• Add up the numbers in the even places (2nd, 4th, 6th, 8th, 10th,12th) and add it to the previous number.

• Take the last digit.• If the last digit in the barcode is not this number, then the bar code is

not valid.

Which of the following bar codes is valid?

1. 9300657111663

X Heinz tomato sauce

2. 9310577280276

× not valid

3. 9300605003811

X Milo

Page 9: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Activity 1: Checking Barcodes

Checking for an error in the code

• There are 13 numbers, the last is the check digit.• Add up the numbers in the odd places (1st, 3rd, 5th, 7th, 9th, 11th)

and multiply by 3.

• Add up the numbers in the even places (2nd, 4th, 6th, 8th, 10th,12th) and add it to the previous number.

• Take the last digit.• If the last digit in the barcode is not this number, then the bar code is

not valid.

Which of the following bar codes is valid?

1. 9300657111663

X Heinz tomato sauce

2. 9310577280276

× not valid

3. 9300605003811

X Milo

Page 10: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Activity 1: Checking Barcodes

Checking for an error in the code

• There are 13 numbers, the last is the check digit.• Add up the numbers in the odd places (1st, 3rd, 5th, 7th, 9th, 11th)

and multiply by 3.• Add up the numbers in the even places (2nd, 4th, 6th, 8th, 10th,

12th) and add it to the previous number.

• Take the last digit.• If the last digit in the barcode is not this number, then the bar code is

not valid.

Which of the following bar codes is valid?

1. 9300657111663

X Heinz tomato sauce

2. 9310577280276

× not valid

3. 9300605003811

X Milo

Page 11: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Activity 1: Checking Barcodes

Checking for an error in the code

• There are 13 numbers, the last is the check digit.• Add up the numbers in the odd places (1st, 3rd, 5th, 7th, 9th, 11th)

and multiply by 3.• Add up the numbers in the even places (2nd, 4th, 6th, 8th, 10th,

12th) and add it to the previous number.• Take the last digit.

• If the last digit in the barcode is not this number, then the bar code isnot valid.

Which of the following bar codes is valid?

1. 9300657111663

X Heinz tomato sauce

2. 9310577280276

× not valid

3. 9300605003811

X Milo

Page 12: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Activity 1: Checking Barcodes

Checking for an error in the code

• There are 13 numbers, the last is the check digit.• Add up the numbers in the odd places (1st, 3rd, 5th, 7th, 9th, 11th)

and multiply by 3.• Add up the numbers in the even places (2nd, 4th, 6th, 8th, 10th,

12th) and add it to the previous number.• Take the last digit.• If the last digit in the barcode is not this number, then the bar code is

not valid.

Which of the following bar codes is valid?

1. 9300657111663

X Heinz tomato sauce

2. 9310577280276

× not valid

3. 9300605003811

X Milo

Page 13: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Activity 1: Checking Barcodes

Checking for an error in the code

• There are 13 numbers, the last is the check digit.• Add up the numbers in the odd places (1st, 3rd, 5th, 7th, 9th, 11th)

and multiply by 3.• Add up the numbers in the even places (2nd, 4th, 6th, 8th, 10th,

12th) and add it to the previous number.• Take the last digit.• If the last digit in the barcode is not this number, then the bar code is

not valid.

Which of the following bar codes is valid?

1. 9300657111663

X Heinz tomato sauce

2. 9310577280276

× not valid

3. 9300605003811

X Milo

Page 14: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Activity 1: Checking Barcodes

Checking for an error in the code

• There are 13 numbers, the last is the check digit.• Add up the numbers in the odd places (1st, 3rd, 5th, 7th, 9th, 11th)

and multiply by 3.• Add up the numbers in the even places (2nd, 4th, 6th, 8th, 10th,

12th) and add it to the previous number.• Take the last digit.• If the last digit in the barcode is not this number, then the bar code is

not valid.

Which of the following bar codes is valid?

1. 9300657111663

X Heinz tomato sauce

2. 9310577280276

× not valid

3. 9300605003811

X Milo

Page 15: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Activity 1: Checking Barcodes

Checking for an error in the code

• There are 13 numbers, the last is the check digit.• Add up the numbers in the odd places (1st, 3rd, 5th, 7th, 9th, 11th)

and multiply by 3.• Add up the numbers in the even places (2nd, 4th, 6th, 8th, 10th,

12th) and add it to the previous number.• Take the last digit.• If the last digit in the barcode is not this number, then the bar code is

not valid.

Which of the following bar codes is valid?

1. 9300657111663 X Heinz tomato sauce

2. 9310577280276

× not valid

3. 9300605003811

X Milo

Page 16: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Activity 1: Checking Barcodes

Checking for an error in the code

• There are 13 numbers, the last is the check digit.• Add up the numbers in the odd places (1st, 3rd, 5th, 7th, 9th, 11th)

and multiply by 3.• Add up the numbers in the even places (2nd, 4th, 6th, 8th, 10th,

12th) and add it to the previous number.• Take the last digit.• If the last digit in the barcode is not this number, then the bar code is

not valid.

Which of the following bar codes is valid?

1. 9300657111663 X Heinz tomato sauce

2. 9310577280276 × not valid

3. 9300605003811

X Milo

Page 17: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Activity 1: Checking Barcodes

Checking for an error in the code

• There are 13 numbers, the last is the check digit.• Add up the numbers in the odd places (1st, 3rd, 5th, 7th, 9th, 11th)

and multiply by 3.• Add up the numbers in the even places (2nd, 4th, 6th, 8th, 10th,

12th) and add it to the previous number.• Take the last digit.• If the last digit in the barcode is not this number, then the bar code is

not valid.

Which of the following bar codes is valid?

1. 9300657111663 X Heinz tomato sauce

2. 9310577280276 × not valid

3. 9300605003811 X Milo

Page 18: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Lying once

Get yourselves into groups of two.

You will be versing each other in a game of secret keeping and lies!

Page 19: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

The Game

The game is played as follows:

1. One of you is the secret keeper , the other is the detective.

2. The secret is a number from 0 to 15.

3. The detective may ask 7 questions with Yes/No answer

4. The secret keeper is allowed to lie at most once.5. After the 7 questions, the detective makes the guess.

• Correct: 1 point• Incorrect: -2 points• No guess: 0 points

6. Three turns at detective work each!

Page 20: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

The Game

The game is played as follows:

1. One of you is the secret keeper , the other is the detective.

2. The secret is a number from 0 to 15.

3. The detective may ask 7 questions with Yes/No answer

4. The secret keeper is allowed to lie at most once.5. After the 7 questions, the detective makes the guess.

• Correct: 1 point• Incorrect: -2 points• No guess: 0 points

6. Three turns at detective work each!

Page 21: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

The Game

The game is played as follows:

1. One of you is the secret keeper , the other is the detective.

2. The secret is a number from 0 to 15.

3. The detective may ask 7 questions with Yes/No answer

4. The secret keeper is allowed to lie at most once.5. After the 7 questions, the detective makes the guess.

• Correct: 1 point• Incorrect: -2 points• No guess: 0 points

6. Three turns at detective work each!

Page 22: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

The Game

The game is played as follows:

1. One of you is the secret keeper , the other is the detective.

2. The secret is a number from 0 to 15.

3. The detective may ask 7 questions with Yes/No answer

4. The secret keeper is allowed to lie at most once.

5. After the 7 questions, the detective makes the guess.• Correct: 1 point• Incorrect: -2 points• No guess: 0 points

6. Three turns at detective work each!

Page 23: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

The Game

The game is played as follows:

1. One of you is the secret keeper , the other is the detective.

2. The secret is a number from 0 to 15.

3. The detective may ask 7 questions with Yes/No answer

4. The secret keeper is allowed to lie at most once.5. After the 7 questions, the detective makes the guess.

• Correct: 1 point• Incorrect: -2 points• No guess: 0 points

6. Three turns at detective work each!

Page 24: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

The Game

The game is played as follows:

1. One of you is the secret keeper , the other is the detective.

2. The secret is a number from 0 to 15.

3. The detective may ask 7 questions with Yes/No answer

4. The secret keeper is allowed to lie at most once.5. After the 7 questions, the detective makes the guess.

• Correct: 1 point• Incorrect: -2 points• No guess: 0 points

6. Three turns at detective work each!

Page 25: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

A Bad Way to Play

1. Is your secret number equal to 0? No

2. Is your secret number equal to 1? No

3. Is your secret number equal to 2? No

4. Is your secret number equal to 3? No

5. Is your secret number equal to 4? No

6. Is your secret number equal to 5? No

7. Is your secret number equal to 6? No

Page 26: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Good Questions

For those who won the game, what questions did you ask?

• Is your number prime?• Is your number even?• Is your number between 0 and 7?• Should we ever ask the same question twice? Or thrice?

Page 27: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Good Questions

For those who won the game, what questions did you ask?

• Is your number prime?

• Is your number even?• Is your number between 0 and 7?• Should we ever ask the same question twice? Or thrice?

Page 28: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Good Questions

For those who won the game, what questions did you ask?

• Is your number prime?• Is your number even?

• Is your number between 0 and 7?• Should we ever ask the same question twice? Or thrice?

Page 29: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Good Questions

For those who won the game, what questions did you ask?

• Is your number prime?• Is your number even?• Is your number between 0 and 7?

• Should we ever ask the same question twice? Or thrice?

Page 30: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Good Questions

For those who won the game, what questions did you ask?

• Is your number prime?• Is your number even?• Is your number between 0 and 7?• Should we ever ask the same question twice? Or thrice?

Page 31: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

A Strategy Against those Quick to Lie

1. Is your number even? NO

If you think they have lied here, then you can beat them!

2. Is your number even? YES

Ok, so they did lie! Ask one more time to be sure if their first orsecond answer was the lie.

3. Is your number even? YES

Can we get their number now?

Page 32: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

A Strategy Against those Quick to Lie

1. Is your number even? NO

If you think they have lied here, then you can beat them!

2. Is your number even? YES

Ok, so they did lie! Ask one more time to be sure if their first orsecond answer was the lie.

3. Is your number even? YES

Can we get their number now?

Page 33: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

A Strategy Against those Quick to Lie

1. Is your number even? NO

If you think they have lied here, then you can beat them!

2. Is your number even? YES

Ok, so they did lie! Ask one more time to be sure if their first orsecond answer was the lie.

3. Is your number even? YES

Can we get their number now?

Page 34: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Detectives

Mathematicians make the best detectives,

• and we will prove this to you now!

• Ok, so it’s not the mathematicians which are good detectives, it’s theerror-correcting codes they create!

Page 35: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Detectives

Mathematicians make the best detectives,

• and we will prove this to you now!• Ok, so it’s not the mathematicians which are good detectives, it’s the

error-correcting codes they create!

Page 36: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Game Theory

Game Theory is the mathematical theory of “how to win games”.

Sometimes, the way we think we should play to win games is not whatwe expected.

A lot of players think about the moment, but you must think about the bigpicture in order to know what’s best!

Page 37: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Game Theory

Game Theory is the mathematical theory of “how to win games”.

Sometimes, the way we think we should play to win games is not whatwe expected.

A lot of players think about the moment, but you must think about the bigpicture in order to know what’s best!

Page 38: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Game Theory

Game Theory is the mathematical theory of “how to win games”.

Sometimes, the way we think we should play to win games is not whatwe expected.

A lot of players think about the moment, but you must think about the bigpicture in order to know what’s best!

Page 39: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Example

1994 Shell Caribbean Cup - Barbados V Grenada

Barbados entered the match, needing to win by 2 goals to progress to thenext round.

This cup had an odd rule, where if a team won on ’golden goal’ it wouldbe recorded as 2-0.

Barbados were winning 2-0, until 5 minutes before full-time whereGrenada made it 2-1.

What happened next...?

Page 40: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Example

1994 Shell Caribbean Cup - Barbados V Grenada

Barbados entered the match, needing to win by 2 goals to progress to thenext round.

This cup had an odd rule, where if a team won on ’golden goal’ it wouldbe recorded as 2-0.

Barbados were winning 2-0, until 5 minutes before full-time whereGrenada made it 2-1.

What happened next...?

Page 41: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Example

1994 Shell Caribbean Cup - Barbados V Grenada

Barbados entered the match, needing to win by 2 goals to progress to thenext round.

This cup had an odd rule, where if a team won on ’golden goal’ it wouldbe recorded as 2-0.

Barbados were winning 2-0, until 5 minutes before full-time whereGrenada made it 2-1.

What happened next...?

Page 42: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Example

1994 Shell Caribbean Cup - Barbados V Grenada

Barbados entered the match, needing to win by 2 goals to progress to thenext round.

This cup had an odd rule, where if a team won on ’golden goal’ it wouldbe recorded as 2-0.

Barbados were winning 2-0, until 5 minutes before full-time whereGrenada made it 2-1.

What happened next...?

Page 43: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Example

1994 Shell Caribbean Cup - Barbados V Grenada

Barbados entered the match, needing to win by 2 goals to progress to thenext round.

This cup had an odd rule, where if a team won on ’golden goal’ it wouldbe recorded as 2-0.

Barbados were winning 2-0, until 5 minutes before full-time whereGrenada made it 2-1.

What happened next...?

Page 44: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Pirates and GoldThere are 5 pirates (A ,B ,C ,D,E) who have found 10 pieces of gold.

A is fiercer than B, who is fiercer than C, who is fiercer than D, who isfiercer than E.

These democratic pirates have rules for this situation. The fiercest pirateA will propose a way to distribute the gold, and they will all (including A )vote on this proposal.

If 50% or more vote for the proposal, then the gold is distributed asproposed.

If less than 50% vote for the proposal, the fiercest pirate gets thrownoverboard, and the democratic process repeats, with B, now the fiercestpirate, making the proposal.

How should A distribute the gold to maximise his takings whilst avoidingbeing thrown overboard?

Assumptions: All pirates are rational, no two pirates are equally fierce,and a pirate always prefers gold to the enjoyment of throwing the fiercestoverboard.

Page 45: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Pirates and GoldThere are 5 pirates (A ,B ,C ,D,E) who have found 10 pieces of gold.

A is fiercer than B, who is fiercer than C, who is fiercer than D, who isfiercer than E.

These democratic pirates have rules for this situation. The fiercest pirateA will propose a way to distribute the gold, and they will all (including A )vote on this proposal.

If 50% or more vote for the proposal, then the gold is distributed asproposed.

If less than 50% vote for the proposal, the fiercest pirate gets thrownoverboard, and the democratic process repeats, with B, now the fiercestpirate, making the proposal.

How should A distribute the gold to maximise his takings whilst avoidingbeing thrown overboard?

Assumptions: All pirates are rational, no two pirates are equally fierce,and a pirate always prefers gold to the enjoyment of throwing the fiercestoverboard.

Page 46: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Pirates and GoldThere are 5 pirates (A ,B ,C ,D,E) who have found 10 pieces of gold.

A is fiercer than B, who is fiercer than C, who is fiercer than D, who isfiercer than E.

These democratic pirates have rules for this situation. The fiercest pirateA will propose a way to distribute the gold, and they will all (including A )vote on this proposal.

If 50% or more vote for the proposal, then the gold is distributed asproposed.

If less than 50% vote for the proposal, the fiercest pirate gets thrownoverboard, and the democratic process repeats, with B, now the fiercestpirate, making the proposal.

How should A distribute the gold to maximise his takings whilst avoidingbeing thrown overboard?

Assumptions: All pirates are rational, no two pirates are equally fierce,and a pirate always prefers gold to the enjoyment of throwing the fiercestoverboard.

Page 47: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Pirates and GoldThere are 5 pirates (A ,B ,C ,D,E) who have found 10 pieces of gold.

A is fiercer than B, who is fiercer than C, who is fiercer than D, who isfiercer than E.

These democratic pirates have rules for this situation. The fiercest pirateA will propose a way to distribute the gold, and they will all (including A )vote on this proposal.

If 50% or more vote for the proposal, then the gold is distributed asproposed.

If less than 50% vote for the proposal, the fiercest pirate gets thrownoverboard, and the democratic process repeats, with B, now the fiercestpirate, making the proposal.

How should A distribute the gold to maximise his takings whilst avoidingbeing thrown overboard?

Assumptions: All pirates are rational, no two pirates are equally fierce,and a pirate always prefers gold to the enjoyment of throwing the fiercestoverboard.

Page 48: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Pirates and GoldThere are 5 pirates (A ,B ,C ,D,E) who have found 10 pieces of gold.

A is fiercer than B, who is fiercer than C, who is fiercer than D, who isfiercer than E.

These democratic pirates have rules for this situation. The fiercest pirateA will propose a way to distribute the gold, and they will all (including A )vote on this proposal.

If 50% or more vote for the proposal, then the gold is distributed asproposed.

If less than 50% vote for the proposal, the fiercest pirate gets thrownoverboard, and the democratic process repeats, with B, now the fiercestpirate, making the proposal.

How should A distribute the gold to maximise his takings whilst avoidingbeing thrown overboard?

Assumptions: All pirates are rational, no two pirates are equally fierce,and a pirate always prefers gold to the enjoyment of throwing the fiercestoverboard.

Page 49: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Pirates and GoldThere are 5 pirates (A ,B ,C ,D,E) who have found 10 pieces of gold.

A is fiercer than B, who is fiercer than C, who is fiercer than D, who isfiercer than E.

These democratic pirates have rules for this situation. The fiercest pirateA will propose a way to distribute the gold, and they will all (including A )vote on this proposal.

If 50% or more vote for the proposal, then the gold is distributed asproposed.

If less than 50% vote for the proposal, the fiercest pirate gets thrownoverboard, and the democratic process repeats, with B, now the fiercestpirate, making the proposal.

How should A distribute the gold to maximise his takings whilst avoidingbeing thrown overboard?

Assumptions: All pirates are rational, no two pirates are equally fierce,and a pirate always prefers gold to the enjoyment of throwing the fiercestoverboard.

Page 50: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Pirates and GoldThere are 5 pirates (A ,B ,C ,D,E) who have found 10 pieces of gold.

A is fiercer than B, who is fiercer than C, who is fiercer than D, who isfiercer than E.

These democratic pirates have rules for this situation. The fiercest pirateA will propose a way to distribute the gold, and they will all (including A )vote on this proposal.

If 50% or more vote for the proposal, then the gold is distributed asproposed.

If less than 50% vote for the proposal, the fiercest pirate gets thrownoverboard, and the democratic process repeats, with B, now the fiercestpirate, making the proposal.

How should A distribute the gold to maximise his takings whilst avoidingbeing thrown overboard?

Assumptions: All pirates are rational, no two pirates are equally fierce,and a pirate always prefers gold to the enjoyment of throwing the fiercestoverboard.

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Error detection Lying once Error Correction Gold and Pirates Class Quiz

Pirates and Gold

Sometimes, the way to best examine a game is to start from the end.

If the game plays on with the proposals being refused then we will end upin the two pirate situation DE. What happens here?

D should propose that he takes all 10 coins, because his vote counts for50%.

Now think about the case with three pirates: CDE

Page 52: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Pirates and Gold

Sometimes, the way to best examine a game is to start from the end.

If the game plays on with the proposals being refused then we will end upin the two pirate situation DE. What happens here?

D should propose that he takes all 10 coins, because his vote counts for50%.

Now think about the case with three pirates: CDE

Page 53: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Pirates and Gold

Sometimes, the way to best examine a game is to start from the end.

If the game plays on with the proposals being refused then we will end upin the two pirate situation DE. What happens here?

D should propose that he takes all 10 coins, because his vote counts for50%.

Now think about the case with three pirates: CDE

Page 54: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Pirates and Gold

Sometimes, the way to best examine a game is to start from the end.

If the game plays on with the proposals being refused then we will end upin the two pirate situation DE. What happens here?

D should propose that he takes all 10 coins, because his vote counts for50%.

Now think about the case with three pirates: CDE

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Error detection Lying once Error Correction Gold and Pirates Class Quiz

Solution

Page 56: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Solution

Page 57: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Solution

Page 58: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Solution

Page 59: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Solution

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Error detection Lying once Error Correction Gold and Pirates Class Quiz

True or False

We are going to do a class quiz.

To answer true to a question, put both hands on top of your head.

To answer false to a question, put both hands on your backside.

If you get an answer wrong, you get to stay in the game but you are nowplaying it kneeling down.

If you get an answer wrong when you’re kneeling, you are out of thegame.

The last person remaining in the game wins the prize!

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Error detection Lying once Error Correction Gold and Pirates Class Quiz

Question 1

The football (soccer) example we looked at before was from the ShellCaribbean Cup in 1994.

TRUE

Page 62: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Question 1

The football (soccer) example we looked at before was from the ShellCaribbean Cup in 1994.

TRUE

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Error detection Lying once Error Correction Gold and Pirates Class Quiz

Question 2

When there are only three pirates CDE, C gets 8, D gets 1, and E gets 0.

FALSE

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Error detection Lying once Error Correction Gold and Pirates Class Quiz

Question 2

When there are only three pirates CDE, C gets 8, D gets 1, and E gets 0.

FALSE

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Error detection Lying once Error Correction Gold and Pirates Class Quiz

Question 3

Alice’s Adventures in Wonderland was written by a mathematician.

TRUE

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Error detection Lying once Error Correction Gold and Pirates Class Quiz

Question 3

Alice’s Adventures in Wonderland was written by a mathematician.

TRUE

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Error detection Lying once Error Correction Gold and Pirates Class Quiz

Question 4

The number 1 is a prime number.

FALSE

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Error detection Lying once Error Correction Gold and Pirates Class Quiz

Question 4

The number 1 is a prime number.

FALSE

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Error detection Lying once Error Correction Gold and Pirates Class Quiz

Question 5

The number 172263 is a prime number.

FALSE

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Error detection Lying once Error Correction Gold and Pirates Class Quiz

Question 5

The number 172263 is a prime number.

FALSE

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Error detection Lying once Error Correction Gold and Pirates Class Quiz

Question 6

There are more valid completed Sudoku grids than all the grains of sandon all the world’s beaches.

TRUE

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Error detection Lying once Error Correction Gold and Pirates Class Quiz

Question 6

There are more valid completed Sudoku grids than all the grains of sandon all the world’s beaches.

TRUE

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Error detection Lying once Error Correction Gold and Pirates Class Quiz

Question 7

0.99999 . . . is exactly equal to the number 1.

TRUE

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Error detection Lying once Error Correction Gold and Pirates Class Quiz

Question 7

0.99999 . . . is exactly equal to the number 1.

TRUE

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Error detection Lying once Error Correction Gold and Pirates Class Quiz

Question 8

In a random group of 23 people, there is a more than 90% chance thatnone of them share a birthday.

FALSE

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Error detection Lying once Error Correction Gold and Pirates Class Quiz

Question 8

In a random group of 23 people, there is a more than 90% chance thatnone of them share a birthday.

FALSE

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Error detection Lying once Error Correction Gold and Pirates Class Quiz

Question 9

The plus sign + was first used in the 13th century.

FALSE

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Error detection Lying once Error Correction Gold and Pirates Class Quiz

Question 9

The plus sign + was first used in the 13th century.

FALSE

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Error detection Lying once Error Correction Gold and Pirates Class Quiz

Question 10

A ’jiffy’ is an actual unit of time for 1/100th of a second.

TRUE

Page 80: Campus Challenge: Brain Games - STUDYSmarter, UWA - Mathsface

Error detection Lying once Error Correction Gold and Pirates Class Quiz

Question 10

A ’jiffy’ is an actual unit of time for 1/100th of a second.

TRUE